Question

Find the value of x and y from the following parallelogram:

Answer 1

Given:

Parallelogram with angles:

Top-left = 3x + y

Top-right = x + y + 10°

Bottom-left = 2x + 5°

In a parallelogram, opposite angles are equal and adjacent angles are supplementary sum to 180°.

Step-wise calculation:

1. Opposite angles equal (top-right = bottom-left):

x + y + 10 = 2x + 5

⇒ y + 10 = x + 5

⇒ y = x – 5

Adjacent angles supplementary (top-left + top-right = 180°):

(3x + y) + (x + y + 10) = 180

⇒ 4x + 2y + 10 = 180

⇒ 4x + 2y = 170

⇒ 2x + y = 85

Substitute y = x – 5 into 2x + y = 85:

2x + (x – 5) = 85

⇒ 3x – 5 = 85

⇒ 3x = 90

⇒ x = 30

Then y = x – 5

= 30 – 5

= 25