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 congruent and the diagonals of a kite are perpendicular. The sum of the interior angles of a quadrilateral is 360°.

Step2: Set up the angle - sum equation

Let's call the known non - right angles 34° and 90°. Let the unknown angles be ∠1 and ∠2. We know that 34°+90° + ∠1+∠2=360°. Also, in a kite, the non - vertex angles between the pairs of congruent sides are equal. So ∠1 = ∠2.

Step3: Solve for the unknown angles

Substitute ∠1 for ∠2 in the equation 34°+90° + ∠1+∠1=360°. Combine like terms: 124° + 2∠1=360°. Subtract 124° from both sides: 2∠1=360° - 124°=236°. Then divide both sides by 2: ∠1 = 118°.

Answer:

118