This handy Math in Focus Grade 5 Workbook Answer Key Chapter 13 Practice 3 Right, Isosceles, and Equilateral Triangles provides detailed solutions for the textbook questions.

## Math in Focus Grade 5 Chapter 13 Practice 3 Answer Key Right, Isosceles, and Equilateral Triangles

**Complete. ABC and EFG are right triangles.**

Question 1.

m∠B =___

m∠A + m∠C = ___

= ____

Answer:

m∠B =90°

m∠A + m∠C = 90°

Explanation:

Properties of Right – Angled Triangle

- One angle of the triangle always measures 90degree.
- The hypotenuse is the longest side of the right-angle triangle.
- The side that is opposite to the 90degree angle is the hypotenuse.
- The Sum of two interior angles of the right-angled triangle is always 90degree.

Question 2.

m∠E = ___

m∠F + m∠G = ___

Answer:

m∠E = 90°

m∠F + m∠G = 90°

Explanation:

Properties of Right – Angled Triangle

- One angle of the triangle always measures 90°.
- The hypotenuse is the longest side of the right-angle triangle.
- The side that is opposite to the 90° angle is the hypotenuse.
- The Sum of two interior angles of the right-angled triangle is always 90degree.

**Measure the angles of the triangle. Then fill in the blanks.**

Question 3.

m∠A _____

m∠B ______

m∠C ______

m∠A + m∠C ______

Answer:

m∠B = 90°

m∠C = 40°

m∠A = 50°

Explanation:

Sum of angles in a triangle are 180°

40 + 90 = 130

180 – 130 = 50

m∠A = 50°

m∠A + m∠C = 50° + 40° = 90°

**These triangles are not drawn to scale. Identify and shade the right triangles.**

Question 4.

Answer:

Explanation:

- One angle of the triangle always measures 90°.
- The hypotenuse is the longest side of the right-angle triangle.
- The side that is opposite to the 90° angle is the hypotenuse.
- The Sum of two interior angles of the right-angled triangle is always 90degree.

**These triangles are not drawn to scale. Find the unknown angle measures.**

Question 5.

Find the sum of the measures of ∠A and ∠B.

Answer:

∠A + ∠B = 90°

Explanation:

Properties of Right – Angled Triangle

- One angle of the triangle always measures 90°.
- The hypotenuse is the longest side of the right-angle triangle.
- The side that is opposite to the 90° angle is the hypotenuse.
- The Sum of two interior angles of the right-angled triangle is always 90degree.

Question 6.

Find the measure of ∠C.

Answer:

33°

Explanation:

Properties of Right – Angled Triangle

- The Sum of two interior angles of the right-angled triangle is always 90degree.

So in right angle triangle, Sum of other two angles is 90°.

So ∠C = 90 – 57 = 33

Question 7.

Find the measure of ∠ADC and ∠ABC.

Answer:

∠ADC =62°

∠ABC =28°

Explanation:

In Triangle DAB, ∠DAB =90°

In Triangle ABC, ∠ACB=90°

In Triangle ACD, ∠ACD=90°

and ∠DAC=28°

So ∠ADC = 180° -(∠ACD +∠DAC) = 180° -(90°+28°) = 180° -(118°) =62°

∠BAC = ∠DAB – ∠DAC = 90° -28° = 62°

∠ABC =180° -(∠ACB +∠BAC) = 180° -(90°+62°) = 180° -(152°) =28°

Question 8.

Find the measures of ∠EGF and ∠DGE.

Answer:

∠EGF =64°

∠DGE = 26°

Explanation:

In Triangle DGF, ∠DGF=90°

In Triangle GEF, ∠GEF=90° and ∠EFG=26°

In Triangle DEG, ∠DEG=90°

So ∠EGF= 180° -(∠GEF+∠EFG) = 180° -(90°+26°) = 180° -(116°) =64°

∠DGE= ∠DGF- ∠EGF= 90° -64° = 26°

**Complete. XYZ and PQR are isosceles triangles.**

Question 9.

Which two sides are of equal length?

________

Which two angles have equal measures?

_________

Answer:

XY and XZ sides are equal length.

∠Z and ∠Y angles have equal measures.

Explanation:

- It has two sides of equal length.
- The angles opposite to equal sides are equal in measure

Question 10.

Which two sides are of equal length?

_________

Which two angles have equal measures?

________

Answer:

PR and QR sides are of equal length.

∠P and ∠Q angles have equal measures.

Explanation:

An Isosceles Triangle has the Following Properties:

- It has two sides of equal length.
- The angles opposite to equal sides are equal in measure

**These triangles are not drawn to scale. Find the unknown angle measures.**

Question 11.

Answer:

Explanation:

The properties of a triangle are:

- The sum of all internal angles of a triangle is always equal to 180
^{°}^{.}This is called the angle sum property of a triangle. So,

1. 180 – (46 + 86) = 48

2. 180 – (75+74) = 31

3. 180 – (64 +52) = 64

4. 180 – (90 + 30 ) = 60

5. 180 – (80 + 80 ) = 20

**These triangles are not drawn to scale. Find the unknown angle measures.**

Question 12.

Find the measure of ∠F.

Answer:

∠F = 74°

Explanation:

The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^{°}^{.}

∠D + ∠F = 180 – 53 = 127 °

So ∠D = ∠E Then ∠D = 53 °

then ∠F = 127 – 53 =74°

Question 13.

Find the measure of ∠C.

Answer:

∠C =72°

Explanation:

The property of a triangle is: The sum of all internal angles of a triangle is always equal to 180^{°}^{.}

∠C + ∠B = 180 – 36 = 144°

An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure

So ∠C = ∠B Then 144/2 =72°

then ∠C =72°

Question 14.

Find the measure of ∠TRS.

Answer:

∠TRS = 180 – (∠RST+∠RTS)=180 – (20+90) = 70°

Explanation:

Triangle URS is a Isosceles Triangle.

An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure Then

∠U= ∠S = 20°

The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^{°}^{.}

In Triangle TRS ,

∠RST = 20°

∠RTS = 90°

∠TRS = 180 – (∠RST+∠RTS)=180 – (20+90) = 70°

Question 15.

Find the measure of ∠d.

Answer:

∠d = 172°

Explanation:

Triangle WXY is a Isosceles Triangle.

An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure Then

then ∠W= ∠Y

Triangle WXZ a Right angle Triangle.

then ∠WZX = 90°

∠WXZ=86°

The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^{°}^{.}

In Triangle WZX,

∠XWZ = 180 – (∠WZX+∠WXZ )=180 – (90+86) = 4°

In Triangle WXY , ∠W= ∠Y = 4°

∠d = 180 – (4+4) = 172°

**Complete. Use your protractor and centimeter ruler to measure the sides and angles. Which figure is an equilateral triangle? Check the box.**

Question 16.

AB = __ cm

BC = __ cm

AC = ___ cm

m∠A = ___

m∠B = ___

m∠C = ____

Answer:

Question 17.

XY = __ cm

YZ = __ cm

XZ = ___ cm

m∠X = ___

m∠Y = ___

m∠Z = ____

Answer:

Explanation:

XY = 4 cm

YZ = 4 cm

XZ = 4 cm

m∠X = 60°

m∠Y = 60°

m∠Z = 60°

Explanation:

The angles and sides are equal

**Complete. ABC is an equilateral triangle.**

Question 18.

Which angles have measures equal to the measure of ∠A?

Answer:

∠A = ∠B = ∠C

Explanation:

- Three sides are equal.
- Three angles are equal i.e 60° each.

Question 19.

Which sides have lengths equal to the length of \(\overline{A B}\)?

Answer:

\(\overline{A B}\)= \(\overline{B C}\) = \(\overline{A C}\)

Explanation:

- Three sides are equal.
- Three angles are equal i.e 60° each.

Question 20.

What can you say about the angles of triangle ABC ?

Answer:

All angles are equal and 60° each.

Explanation:

- Three sides are equal.
- Three angles are equal i.e 60° each.

**These triangles are not drawn to scale. Identify and shade the equilateral triangles.**

Question 21.

Answer:

Explanation:

Properties of an Equilateral Triangle

- Three sides are equal.
- Three angles are equal i.e 60° each.

**These triangles are not drawn to scale. Find the unknown angle measures.**

Question 22.

Find the measure of ∠Q.

Answer:

∠Q = 60°

Explanation:

The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^{°}^{.}

∠Q = 180 – ∠P + ∠R = 180 – 60 + 60 = 60°

Question 23.

Find the measures of ∠Y and ∠Z

Answer:

∠Y =∠Z= 60°

Explanation:

The property of a triangle is : The sum of all internal angles of a triangle is always equal to 180^{°}^{.}

∠Z + ∠Y = 180 – ∠X = 180 – 60 = 120°

As per diagram Triangle XYZ is a Isosceles Triangle.

An Isosceles Triangle has the Following Property: The angles opposite to equal sides are equal in measure Then

∠Y =∠Z

then ∠Y =∠Z= 120°/2 = 60°

**These triangles are not drawn to scale. Find the unknown angle measures.**

Question 24.

WX = XY = YW. Find the measure of ∠d.

Answer:

Explanation:

WX = XY = YW So Triangle WXY is a Equilateral Triangle So Three angles are equal

∠WXY = 60°

∠XWY= 60°

∠WYX= 60°

So In Triangle XYZ,

∠ZXY= 60°

∠XZY= 90°

∠XYZ= 180 – 90 + 60=30°

∠d = ∠WYX -∠XYZ =60 – 30 =30°

Question 25.

Find the measure of ∠e.

Answer:

∠e = 120°

Explanation:

∠LON = 90° given

As the triangle is equalateral the angles are equal

so the measure of ∠LOE = 60°

∠LMO = 60°

NOM triangle is an isosceles triangle

90 – 60 = 30°

∠MON = 30°

∠OMN = 30°

30° + 30° = 60°

180° – 60° = 120°

∠e = 120°

Question 26.

Triangle PQR is an equilateral triangle. Triangle PST is an isosceles triangle. The measures of ∠a, ∠b, and ∠c are the same. Find the measure of ∠d.

Answer:

∠d. = 80°

Explanation:

Triangle PQR is an equilateral triangle.

In equilateral triangle all angles are equal

sum of angles in a triangle are 180°

Triangle PST is an isosceles triangle.

The measures of ∠a, ∠b, and ∠c are the same.

so, ∠a, ∠b, and ∠c = 60°

20° + 20° + 20° = 60°

In isosceles triangle

The isosceles triangle property states that when two sides are equal, the base angles are also equal

so, 180° – 20° = 160°

80° + 80 °= 160°

∠d. = 80°