Question

in the given triangle, ( ab = ac ) and ( angle abc ) has a measure of ( 67^{circ} ). what is the value of ( x )?

Explanation:

Step1: Use the property of isosceles triangle

Since \(AB = AC\), \(\angle ABC=\angle ACB = 67^{\circ}\).

Step2: Apply the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(x=\angle BAC\). Then \(x + 67^{\circ}+67^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(67^{\circ} + 67^{\circ})$$

$$x=180^{\circ}-134^{\circ}$$

$$x = 46^{\circ}$$

Answer:

\(46^{\circ}\)