PROBLEMS ON CORRESPONDING ANGLES

Find the unknown angle measures.

Problem 1 :

Solution :

Angle c and 103 are in corresponding positions. So, they are equal.

∠c = 103

Problem 2 :

Solution :

Angle 130 and b are in corresponding positions. So, they are equal.

∠b = 103

Problem 3 :

Solution :

Angles y and x are in corresponding positions.

y = x

x and 39° are vertically opposite angles.

x = 39° (Vertically opposite angles)

y = 39° (Corresponding angles)

Problem 4 :

Solution :

120 and a° are linear pair.

120 + a = 180

a = 180 - 120

a = 60

a and b are in corresponding positions.

a = b = 60

Problem 5 :

Solution :

Angles x° and 146° are in corresponding positions.

x = 146°

Angles x and y are in corresponding positions.

x = y = 146°

Problem 6 :

Solution :

Angles a and 125 are linear pairs.

a + 125 = 180

a = 180 - 125

a = 55°

b and a are in corresponding positions.

a = b = 55°

Problem 7 :

Solution :

a = 120°, because they are vertically opposite angles.

a = b, because they are corresponding angles.

b and c are linear pair. So,

b + c = 180

120 + c = 180

c = 180 - 120

c = 60°

Again c and d are corresponding angles. So, c = d = 60°

Problem 8 :

Solution :

In the triangle given above,

a and 80° corresponding angles.

So, a = 80°

In the triangle, the sum of interior angles of triangle is 180°.

50 + a + b = 180

50 + 80 + b = 180

130 + b = 180

b =180 - 130

b = 50

Problem 9 :

Solution :

Angles a and 65° are in corresponding positions.

a = 65°

In the triangle,

75 + a + c = 180

75 + 65 + c = 180

140 + c = 180

c = 180 - 140

c = 40

65 + b + c = 180 (linear pair)

65 + b + 40 = 180

105 + b = 180

b = 180 - 105

b = 75

Problem 10 :

Solution :

We have two parallel sides, so one of the angle measure inside the small triangle is 50.

70 + a + 50 = 180

120 + a = 180

a = 180 - 120

a = 60

Problem 11 :

The stairs have a 45° incline. At what angles do you need to attach a rail to two parallel posts so that the rail is parallel to the incline of the steps?

Solution :

∠1 + 45 = 90

∠1 = 90 - 45

∠1 = 45

∠2 = 45 (alternate interior angle for ∠1)

∠3 = 45 + 90

∠3 = 135

∠3 = ∠7 = 135

∠2 = ∠6

∠4 = 135

∠5 = 45

Problem 12 :

Complete the statement. Explain your reasoning.

a) If the measure of ∠1 = 124°, then the measure of ∠4 =

b) If the measure of ∠2 = 48°, then the measure of ∠3 =

c) If the measure of ∠4 = 55°, then the measure of ∠2 =

d) If the measure of ∠6 = 120°, then the measure of ∠8 =

e) If the measure of ∠7 = 50.5°, then the measure of ∠6 =

f) If the measure of ∠3 = 118.7°, then the measure of ∠2 =

Solution :

a) ∠1 = 124°

∠1 and ∠4 are co-interior angles, then 124 + ∠4 = 180

∠4 = 180 - 124

∠4 = 56

b) ∠2 = 48°

∠2 + ∠3 = 180

48 + ∠3 = 180

∠3 = 180 - 48

= 132

c) ∠4 = 55°, ∠2 = ∠4 (Alternate interior angles)

d) ∠6 = 120°

• ∠1 = ∠6 (vertically opposite angles)
• ∠1 = ∠8 (Corresponding angles)

e) ∠7 = 50.5°

∠7 = ∠2 (Corresponding angles)

∠2 + ∠6 = 180

50.5 + ∠6 = 180

∠6 = 180 - 50.5

∠6 = 129.5

f) ∠3 = 118.7°

∠3 and ∠2 are co-interior angles.

∠3 + ∠2 = 180

118.7 + ∠2 = 180

∠2 = 180 - 118.7

∠2 = 61.3

Problem 13 :

A rainbow forms when sunlight reflects off raindrops at different angles. For blue light, the measure of ∠2 is 40°. What is the measure of ∠1?

Solution :

Given that ∠2 is 40°.

∠2 and ∠1 are alternate interior angles. Then they must be equal. So, ∠1 = 40 degree.

Problem 14 :

In a park, a bike path and a horse riding path are parallel. In one part of the park, a hiking trail intersects the two paths. Find the measures of ∠1 and ∠2. Explain your reasoning.

Solution :

∠2 and 72 degree are co-interior angles.

∠2 + 72 = 180

∠2 = 180 - 72

∠2 = 108