This handy Math in Focus Grade 4 Workbook Answer Key Chapter 11 Practice 2 Properties of Squares and Rectangles detailed solutions for the textbook questions.

## Math in Focus Grade 4 Chapter 11 Practice 2 Answer Key Properties of Squares and Rectangles

**All the figures are rectangles. Find the measures of the unknown angles.**

Example

Find the measure of ∠a.

Question 1.

Find the measure of ∠b.

Answer:

Measure of ∠b = 90^{0} – 27^{0}

**∠b= 63**^{0
}Explanation:

A Rectangle is a four sided-polygon, having all the internal angles equal to** 90 degrees**. The two sides at each corner or vertex, meet at right angles. Subtract 27^{0 }from 90^{0}the difference is equal to 63^{0}.

Question 2.

Find the measure of ∠c.

Answer:

Measure of ∠c = 90^{0} – 45 ^{0}

**∠c= 45**^{0
}Explanation:

A Rectangle is a four sided-polygon, having all the internal angles equal to** 90 degrees**. The two sides at each corner or vertex, meet at right angles. Subtract 45^{0 }from 90^{0}the difference is equal to 45^{0}.

**All the figures are rectangles. Find the measures of the unknown angles.**

Question 3.

Find the measure of ∠p.

Answer:

Measure of ∠p = 90^{0} – 36^{0}– 18^{0}

**∠p= 36**^{0
}Explanation:

A Rectangle is a four sided-polygon, having all the internal angles equal to** 90 degrees**. The two sides at each corner or vertex, meet at right angles. Subtract 36^{0} and 18^{0 }from 90^{0}the difference is equal to 36^{0}.

Question 4.

Find the measure of ∠m.

Answer:

Measure of ∠m = 90^{0} – 39^{0}– 22^{0}

**∠m= 29**^{0
}Explanation:

A Rectangle is a four sided-polygon, having all the internal angles equal to** 90 degrees**. The two sides at each corner or vertex, meet at right angles. Subtract 39^{0} and 22^{0 }from 90^{0}the difference is equal to 29^{0}.

**The figure is a rectangle. Find the measure of the unknown angle.**

Question 5.

Find the measure of ∠s.

Answer:

Measure of ∠s = 90^{0} – 25^{0}– 12^{0}

**∠s= 53**^{0
}Explanation:

A Rectangle is a four sided-polygon, having all the internal angles equal to** 90 degrees**. The two sides at each corner or vertex, meet at right angles. Subtract 25^{0} and 12^{0 }from 90^{0}the difference is equal to 53^{0}.

**Find the lengths of the unknown sides.**

Question 6.

The figure is made up of a rectangle and a square. Find BC and GE.

Answer:

In the above image we can observe rectangle and a square.

From the rectangle ABFG we know that

GA = BF = 12 cm

AB = FG = 15cm

From the square CDEF we know that

CD = DE = EF = FC = 8 cm

**BC = GA – CF**

BC = 12 – 8

**BC = 4 cm
GE = AB + EF
**GE = 15 + 8

GE = 23 cm

GE = 23 cm

**Find the lengths of the unknown sides.**

Question 7.

The figure is made up of two rectangles. Find BD and FG.

Answer:

In the above image we can observe two rectangles.

From the rectangle ABCG we know that

AB = CG = 20 feet

BC = GA = 17 feet

From the rectangle CDEF we know that

CD = EF = 5 feet

DE = FC = 14 feet

**BD = BC + CD**

BD = 17 + 5

**BD = 22 feet**

**FG = AB – FC**

FG = 20 – 14

**FG = 6 feet**

Question 8.

The figure is made up of two rectangles. Find QR and RT.

Answer:

In the above image we can observe two rectangles.

From the rectangle PQRS we know that

PQ = RS = 5 yards

QR = SP

From the rectangle STUV we know that

ST = UV = 6 yards

TU = VS = 4 yards

**QR = PV + VS**

QR = 3 + 4

**QR = 7 yards**

**RT = RS + ST**

RT = 5 + 6

**RT = 11 yards**

**Find the lengths of the unknown sides.**

Question 9.

The figure is made up of two rectangles. Find FG.

Answer:

In the above image we can observe two rectangles.

From the rectangle ABGH we know that

BG = HA = 5 miles

AB = GH

From the rectangle CDEF we know that

DE = FC = 8 miles

CD = EF

CG = HA – BC

CG = 5 – 3

**CG = 2 miles**

**FG = DE – CG
**FG = 8 – 2

**FG = 6 miles**

Question 10.

The figure is made up of a square and a rectangle. Find BC.

Answer:

In the above image we can observe rectangle and a square.

From the rectangle ABGH we know that

BG = HA = 10 feet

AB = GH

From the square CDEF we know that

CD = DE = EF = FC = 4 feet

**BC = HA – FC – FG
**BC = 10 – 4 – 2

**BC = 4 feet**