Question

In the figure, L || m and x and y are complementary angles. Find x and y.

(A) 50°, 40° (B) 20°, 70°​

(C) 10°, 80° (D) 30°, 60°​

Answer 1

X and y are complementary angles

so ,

x+y = 90

here , x + 50 and y-20 are alternative angles

therefore,

x+50 = y-20

x +70 = y

y - x = 70

(x+y) + (x - y) = 90 + 70

2x = 160

x = 160/2

x = 80

x +y = 90

80 + y = 90

y = 90- 80

y = 10

y , x = 10 , 80

hope it helps...

Answer 2

Given:

• Line l is parallel to m
• x and y are complimentary angles.

To find:

Value of x and y

Solution:

Since x and y are complimentary angles, they sum up to 90°.

→ x + y = 90°

→ x = 90 - y ----- [Equation 1]

Since line l is parallel to line m,

By Alternate Interior angles;

x + 50 = y - 20

⇒ (90 - y) + 50 = y - 20

⇒ 140 - y = y - 20

⇒ 140 + 20 = y + y

⇒ 2y = 160

⇒ y = 160 ÷ 2

⇒ y = 80°

Substitute the value of y in Equation 1 to find out the value of x.

x = 90 - y

➝ x = 90 - 80

➝ x = 10°

Therefore:

• x = 10°
• y = 80°