Question

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

Explanation:

Step1: Recall kite - angle properties

In a kite, one pair of opposite angles are equal and the diagonals of a kite are perpendicular. Also, the sum of the interior angles of a quadrilateral is 360°.

Step2: Set up an equation for angle - sum

Let's assume the given angles of the kite are 34°, 90°, ∠1, and ∠2. We know that one of the properties of a kite is that one pair of non - adjacent angles are equal. Let's assume the 34° angles are a pair of equal angles.
The sum of the interior angles of a quadrilateral is given by the formula \(S=(4 - 2)\times180^{\circ}=360^{\circ}\).
So, \(34^{\circ}+90^{\circ}+\angle1+\angle2 = 360^{\circ}\). Since the diagonals of a kite are perpendicular, we know that the angles formed by the diagonals are 90°. In a kite, we can also use the fact that the non - right angles come in pairs. If the given non - right angle is 34°, then the other non - right angle (∠1) is also 34°.

Answer:

34