Question

find the measures of the numbered angles in the kite.
the figure is not drawn to scale.
m∠1 = 118° (type an integer or a decimal.)
m∠2 = (type an integer or a decimal.)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Find the measure of angle 2

In the right - angled triangle containing angle 2 and the 34° angle, we know one angle is 90° and another is 34°. Let \(m\angle2=x\). Then, using the angle - sum property of a triangle \(x + 34^{\circ}+90^{\circ}=180^{\circ}\).
We can solve for \(x\) as follows:
\[

$$\begin{align*} x&=180^{\circ}-(90^{\circ} + 34^{\circ})\\ x&=180^{\circ}-124^{\circ}\\ x& = 56^{\circ} \end{align*}$$

\]

Answer:

56