Question

properties of kites
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question
find the measure of angle w.
answer
attempt 1 out of 2
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Explanation:

Step1: 四边形内角和

四边形内角和为\(360^{\circ}\)。

Step2: 等腰三角形性质

在风筝形（一种特殊四边形）中，\(\angle Y\)与\(\angle W\)相邻两边相等，\(\angle U\)与\(\angle V\)相邻两边相等。根据风筝形性质，\(\angle Y\)与\(\angle W\)不相邻的角\(\angle U\)与\(\angle V\)分别相等。已知\(\angle Y = 65^{\circ}\)，\(\angle V=77^{\circ}\)。

Step3: 计算\(\angle W\)

设\(\angle W=x\)，根据四边形内角和公式\(\angle Y+\angle W+\angle V + \angle U=360^{\circ}\)，又因为\(\angle U = \angle V = 77^{\circ}\)（等腰性质），则\(65^{\circ}+x + 77^{\circ}+77^{\circ}=360^{\circ}\)，即\(x+219^{\circ}=360^{\circ}\)，移项可得\(x = 360^{\circ}-219^{\circ}\)。

Answer:

\(141^{\circ}\)