Question

Lines AB and CD are straight lines. Find x and y. Give reasons to justify your solutions.

Answer 1

The measure of angle x = 27°

The measure of angle y =38°

Explanation:

Given: ∠AOM = 90°

⇒ x + ∠MON = 90°

or, x = 90° - ∠MON

= 90° - 63° = 27°

Hence, the measure of x = 27°

Now, as the lines AB and CD intersect each other ,

The pair of angles ∠COB and ∠AOD form a pair of VERTICALLY OPPOSITE ANGLES.

⇒∠COB = ∠AOD (Vertical Angles)

or, 128° = x + 63° + y

From, above : 128° = 27 + 63° + y

or, y = 128° - 90° = 38°

or, the measure of angle y =38°.