Questions: In the diagram below, AD bisects CAB, m ADB=96° and m CAB=60°. Find m C.

In the diagram below, AD bisects CAB, m ADB=96° and m CAB=60°. Find m C.
Transcript text: In the diagram below, $\overline{A D}$ bisects $\angle C A B, \mathrm{~m} \angle A D B=96^{\circ}$ and $\mathrm{m} \angle C A B=60^{\circ}$. Find $\mathrm{m} \angle C$.
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Solution

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Solution Steps

Step 1: Find m∠CAD

Since AD bisects ∠CAB, we have m∠CAD = m∠BAD. We are given that m∠CAB = 60°. Therefore, m∠CAD = m∠BAD = 60°/2 = 30°.

Step 2: Find m∠ADB

We are given that m∠ADB = 96°.

Step 3: Find m∠ACD

In triangle ADC, the sum of the angles is 180°. We know m∠CAD = 30° and m∠ADB = 96°. The exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles. Therefore, m∠ADB = m∠ACD + m∠CAD.

96° = m∠ACD + 30°

m∠ACD = 96° - 30° = 66°

Final Answer

\\(\boxed{66^\circ}\\)

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