Question

The measure of <ACD is 120. Find the measure of <ACB, <BCD, and <ACE.

Explain how you found the measure of <ACE.​

Answer 1

m∠ACB = 39°

m∠BCD = 81°

m∠ACE = 60°

Explanation:

From the picture attached,

m∠ACD = 120°

Since, m∠ACD = m∠ACB + m∠BCD

x + (2x + 3) = 120°

3x + 3 = 120

3x = 117

x = 39

Therefore, m∠ACB = 39°

m∠BCD = (2x + 3) = 2(39) + 3

= 81°

Since, m∠ACE + m∠ACB + m∠BCD = 180° [Angles formed at a point on a straight line]

m∠ACE + 39 + 81 = 180

m∠ACE = 180 - 120

m∠ACE = 60°