Question

find the measure of each angle indicated. 21)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the upper - triangle, we first find the non - marked angle. Let the non - marked angle in the upper - triangle be $x$. Then $x=180^{\circ}-(32^{\circ}+34^{\circ})$.
$x = 180^{\circ}-66^{\circ}=114^{\circ}$.

Step2: Use vertical angles and angle - sum property

The non - marked angle in the upper - triangle and the angle adjacent to the unknown angle in the lower - triangle are vertical angles. So they are equal. Let the unknown angle be $y$. In the lower - triangle, we know that the sum of its interior angles is 180°. So $y = 180^{\circ}-(39^{\circ}+114^{\circ})$.
$y=180^{\circ}-153^{\circ}=27^{\circ}$.

Answer:

$27^{\circ}$