Question

find the measure of each missing angle:

Explanation:

Step1: Find angle 2

Use vertical - angle property. Angle 2 and the 49° angle are vertical angles, so they are equal.
$\angle2 = 49^{\circ}$

Step2: Find angle 1

In the left - hand triangle, use the angle - sum property of a triangle ($\angle1+\angle2 + 68^{\circ}=180^{\circ}$). Substitute $\angle2 = 49^{\circ}$ into the equation.
$\angle1=180^{\circ}-49^{\circ}-68^{\circ}=63^{\circ}$

Step3: Find angle 3

Use the linear - pair property. The angle adjacent to 93° and angle 3 form a linear pair, so $\angle3 = 180^{\circ}-93^{\circ}=87^{\circ}$

Step4: Find angle 4

In the right - hand triangle, use the angle - sum property of a triangle ($\angle3+\angle4 + 49^{\circ}=180^{\circ}$). Substitute $\angle3 = 87^{\circ}$ into the equation.
$\angle4=180^{\circ}-87^{\circ}-49^{\circ}=44^{\circ}$

Answer:

$\angle1 = 63^{\circ}$, $\angle2 = 49^{\circ}$, $\angle3 = 87^{\circ}$, $\angle4 = 44^{\circ}$