Question

find the measures of the numbered angles in the kite. the figure is not drawn to scale. m∠1 = 51° (type an integer or a decimal.)

Explanation:

Step1: Recall kite - angle properties

In a kite, the diagonals are perpendicular. So the angle formed by the diagonals is 90°. Also, a kite has one pair of non - vertex angles that are congruent and the diagonal bisects the vertex angles.

Step2: Find angle 1

We know that one of the non - right angles in the right - triangle formed by the diagonals and the sides of the kite is 26°. Using the fact that the sum of the interior angles of a triangle is 180°. In a right - triangle with one angle 90° and another 26°, for angle 1:

$$m\angle1=180^{\circ}-90^{\circ}-26^{\circ}$$

$$m\angle1 = 64^{\circ}$$

Answer:

64°