Question

Lines

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

Answer 1

x = 14

y = 54

Explanation:

m∠AON = m∠MON - m∠MOA

= 90°- 72°

= 18°

Since, ∠AOD ≅ ∠BOC [Vertically opposite angles]

2x° + 18° = 3x°

3x - 2x = 18

x = 18

Since, ∠BOC, ∠COM and ∠AOM are the linear angles,

m∠BOC + m∠COM + m∠MOA = 180°

3x + y + 72° = 180°

3x + y = 180 - 72

3x + y = 108

3(18) + y = 108

54 + y = 108

y = 108 - 54

y = 54