Question

find the measures of the following angles in the kite shown below. note: figure may not be drawn to scale. a = b =

Explanation:

Step1: Use the property of a kite (equal adjacent sides)

In a kite, one pair of opposite angles are equal. Here, the angles adjacent to the unequal sides are equal. So, \(a = 61^{\circ}\) (since the sides adjacent to \(a\) and \(61^{\circ}\) are equal in length as per the markings).

Step2: Use the angle - sum property of a quadrilateral

The sum of interior angles of a quadrilateral is \(360^{\circ}\). Let's find \(b\). We know three angles: \(a = 61^{\circ}\), one angle is \(101^{\circ}\), and another is \(61^{\circ}\).

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Answer:

\(a = 61\), \(b = 137\)