Question

1. find all missing angles. m - 2 1 72° 57° 3 2 4 o 9 o 45 o 90 o 18

Explanation:

Step1: Find angle 2

In the right - angled triangle with the $72^{\circ}$ angle, since the sum of angles in a triangle is $180^{\circ}$ and one angle is $90^{\circ}$, then $\angle2=180^{\circ}-90^{\circ}-72^{\circ}=18^{\circ}$.

Step2: Find angle 3

$\angle3$ and the $57^{\circ}$ angle are vertical angles, so $\angle3 = 57^{\circ}$.

Step3: Find angle 4

In the larger triangle, we know one angle is $90^{\circ}$, $\angle3 = 57^{\circ}$, and we want to find $\angle4$. Using the angle - sum property of a triangle ($180^{\circ}$ for the sum of interior angles), $\angle4=180^{\circ}-90^{\circ}-57^{\circ}=33^{\circ}$. But we are asked for $\angle2$ which is $18^{\circ}$.

Answer:

18