Question

1. m∠1 = ______ m∠2 = ____ m∠3 = ______ 118° 1 73° 49° 2 3

Explanation:

Step1: Find $m\angle1$

Use the property of linear - pair of angles. A linear - pair of angles sums to $180^{\circ}$. So, $m\angle1=180^{\circ}-118^{\circ}=62^{\circ}$.

Step2: Find the third angle of the large triangle

Let the third angle of the large triangle be $x$. Using the angle - sum property of a triangle ($180^{\circ}$ in a triangle), we have $x = 180^{\circ}-(62^{\circ}+73^{\circ})=45^{\circ}$.

Step3: Find $m\angle2$

Use the angle - sum property of the smaller triangle on the left. Let the angles of the smaller left - hand triangle be $m\angle1$, $m\angle2$ and the third angle of the large triangle. So, $m\angle2=180^{\circ}-(62^{\circ}+45^{\circ}) = 73^{\circ}$.

Step4: Find $m\angle3$

Use the property of linear - pair of angles for the angle adjacent to $m\angle3$. The angle adjacent to $m\angle3$ and the $49^{\circ}$ angle are linear - pair. Let the angle adjacent to $m\angle3$ be $y$, so $y = 180^{\circ}-49^{\circ}=131^{\circ}$. Then, using the angle - sum property of the right - hand triangle, $m\angle3=180^{\circ}-(73^{\circ}+131^{\circ}) = 76^{\circ}$.

Answer:

$m\angle1 = 62^{\circ}$
$m\angle2 = 73^{\circ}$
$m\angle3 = 76^{\circ}$