Question

In the diagram below, the lines are parallel. m∠BCD = 52° and m∠EAB = 73°. What is the measure of ∠ABC?

Answer 1

235°

Explanation:

∠EAB = 73

∠BCD = 52

125

∠ABC = 360 - 125

= 235°

Answer 2

• 235°

Explanation:

Given

• AB ║ CD
• m∠BCD = 52°
• m∠EAB = 73°

To find

• m∠ABC = ?

Solution

Imagine line BF parallel to both AB and CD

Then

• m∠ABC = m∠ABF + m∠CBF
• m∠ABC = (180° - m∠EAB) + (180° - m∠BCD)
• m∠ABC = (180° - 73°) + (180° - 52°) = 107° + 128° = 235°