Question

1. find the measure of each missing angle. 4 points

68° 2 49°
1
3 93°
m∠1 = ____
m∠2 = ____
m∠3 = ____
m∠4 = ____

Explanation:

Step1: Find $m\angle2$ using vertical - angle property

Vertical angles are equal. $\angle2$ and the $49^{\circ}$ angle are vertical angles. So $m\angle2 = 49^{\circ}$.

Step2: Find $m\angle1$ using triangle - angle sum property

In the left - hand triangle, the sum of interior angles of a triangle is $180^{\circ}$. Let the angles of the left - hand triangle be $68^{\circ}$, $m\angle1$, and $m\angle2$. We know $m\angle2 = 49^{\circ}$. Then $m\angle1=180^{\circ}-68^{\circ}-49^{\circ}=63^{\circ}$.

Step3: Find $m\angle3$ using linear - pair property

$\angle3$ and the $93^{\circ}$ angle form a linear pair. A linear pair of angles sums to $180^{\circ}$. So $m\angle3 = 180^{\circ}-93^{\circ}=87^{\circ}$.

Step4: Find $m\angle4$ using triangle - angle sum property

In the right - hand triangle, the sum of interior angles is $180^{\circ}$. Let the angles be $m\angle3 = 87^{\circ}$, $49^{\circ}$, and $m\angle4$. Then $m\angle4=180^{\circ}-87^{\circ}-49^{\circ}=44^{\circ}$.

Answer:

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