Question

find the exterior angle measure
find the measure of ∠acd.

• ∠acd is an exterior angle of △abc.
• ∠acb is adjacent to ∠acd, so ∠abc and ∠bac are the remote interior angles to ∠acd.
• the sum of remote interior angle measures are equal to the exterior angle measure.

m∠abc + m∠bac = m∠acd
96° + 28° = m∠acd

video questions
multiple choice
03:20
what is the measure of ∠acd?
this question is worth 1 point(s)
68 degrees
124 degrees
134 degrees
submit response
em2 grade 8 module 2 lesson 15

Explanation:

Step1: Recall Exterior Angle Theorem

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent (remote interior) angles.

Step2: Identify Angles

In $\triangle ABC$, $\angle ACD$ is an exterior angle. The two remote interior angles are $\angle ABC$ (with measure $96^{\circ}$) and $\angle BAC$ (with measure $28^{\circ}$).

Step3: Calculate $m\angle ACD$

Using the exterior angle theorem, $m\angle ACD=m\angle ABC + m\angle BAC$. Substitute the given values: $m\angle ACD = 96^{\circ}+ 28^{\circ}=124^{\circ}$.

Answer:

124 degrees (the option with 124 degrees)