Question

triangle abc, shown in the diagram below, is an isosceles triangle where $overline{ab}congoverline{ac}$. what is the measure, in degrees, of $angle cab? 43^{circ} 89^{circ} 115^{circ} 50^{circ}$

Explanation:

Step1: Find ∠ACB

Since ∠ACD = 115° and ∠ACB + ∠ACD=180° (linear - pair of angles), then ∠ACB = 180° - 115° = 65°.

Step2: Use the property of isosceles triangle

In isosceles triangle ABC with AB = AC, ∠ABC=∠ACB = 65°.

Step3: Calculate ∠CAB

Using the angle - sum property of a triangle (∠CAB+∠ABC + ∠ACB = 180°), we substitute ∠ABC = 65° and ∠ACB = 65° into the formula. So ∠CAB=180°-(65° + 65°)=50°.

Answer:

50°