Question

From the adjoining figure, find the values of x and y.

Answer 1

Given:

• Quadrilateral ABCD with the side‑markings shown pairs of adjacent sides equal, so AC is the symmetry diagonal and therefore AC bisects ∠A and ∠C kite property.
• At A the two parts are 2x and 32° so they are equal halves of ∠A.
• At C the two parts are 45° and 4y + 5 so they are equal halves of ∠C.

Step-wise calculation:

1. From ∠A being bisected: 

2x = 32 

⇒ `x = 32/2`

⇒ x = 16

2. From ∠C being bisected: 

4y + 5 = 45

⇒ 4y = 45 − 5

⇒ 4y = 40

⇒ `y = 40/4`

⇒ y = 10

x = 16 and y = 10.