Question

find the measure of angle 4

Explanation:

Step1: Identify isosceles - triangle

The triangle with the $68^{\circ}$ angle is isosceles. So the other non - base angle is also $68^{\circ}$.

Step2: Calculate base - angle of isosceles triangle

The sum of interior angles of a triangle is $180^{\circ}$. Let the base - angle be $x$. Then $x=\frac{180 - 68\times2}{2}=\frac{180 - 136}{2}=22^{\circ}$.

Step3: Use vertical - angle property

Angle 4 and the base - angle of the isosceles triangle are vertical angles. Vertical angles are equal. So angle 4 is $22^{\circ}$.

Answer:

22