Question

find the measure of each missing angle. m∠1 = _ m∠2 = _ m∠3 =

Explanation:

Step1: Find $m\angle1$

In the right - triangle with an angle of $38^{\circ}$, using the angle - sum property of a triangle ($180^{\circ}$ in a triangle). Since one angle is $90^{\circ}$ and another is $38^{\circ}$, then $m\angle1=180^{\circ}-90^{\circ}-38^{\circ}=52^{\circ}$.

Step2: Find $m\angle3$

The large triangle has an angle of $63^{\circ}$ and the right - angle. Using the angle - sum property of a triangle, the third angle of the large triangle is $180^{\circ}-90^{\circ}-63^{\circ} = 27^{\circ}$. So $m\angle3 = 27^{\circ}$.

Step3: Find $m\angle2$

We know that the non - right angles of the two triangles at the common vertex must sum up. The angle adjacent to $\angle2$ in the large triangle is $27^{\circ}$ and in the small triangle is $38^{\circ}$. So $m\angle2=38^{\circ}-27^{\circ}=11^{\circ}$.

Answer:

$m\angle1 = 52^{\circ}$
$m\angle2 = 11^{\circ}$
$m\angle3 = 27^{\circ}$