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 property

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

Step2: Calculate angle 1

We know that one of the angles is 90° and another is 34°. Let's consider the sum of the interior angles of the quadrilateral. Let the unknown angles be ∠1 and ∠2.
The sum of the interior angles of a quadrilateral \(S = 360^{\circ}\).
We know that one angle \(A = 90^{\circ}\) and another angle \(B=34^{\circ}\).
Since the diagonals of a kite are perpendicular, we can use the angle - sum property.
The non - right angles of a kite are equal. So, \(\angle1=\angle2\).
We have \(34^{\circ}+90^{\circ}+\angle1+\angle2 = 360^{\circ}\). Since \(\angle1=\angle2\), we can rewrite it as \(34^{\circ}+90^{\circ}+2\angle1 = 360^{\circ}\).
First, simplify the left - hand side: \(124^{\circ}+2\angle1 = 360^{\circ}\).
Then, subtract 124° from both sides: \(2\angle1=360^{\circ}- 124^{\circ}=236^{\circ}\).
Divide both sides by 2: \(\angle1=\frac{236^{\circ}}{2}=118^{\circ}\).

Answer:

118