Question

5 find the measure of each numbered angle: 12° 1 59° 2 3

Explanation:

Step1: Find $\angle 1$

In the right triangle, the sum of angles is $180^\circ$. One angle is $90^\circ$, another is $59^\circ$. So $\angle 1 = 180^\circ - 90^\circ - 59^\circ = 31^\circ$.

Step2: Find $\angle 2$

$\angle 2$ and $59^\circ$ are supplementary (form a linear pair). So $\angle 2 = 180^\circ - 59^\circ = 121^\circ$.

Step3: Find $\angle 3$

In the triangle with angles $12^\circ$, $\angle 2$, and $\angle 3$, sum of angles is $180^\circ$. So $\angle 3 = 180^\circ - 12^\circ - 121^\circ = 49^\circ$.

Answer:

$\angle 1 = 31^\circ$, $\angle 2 = 121^\circ$, $\angle 3 = 49^\circ$