Answer:
Explanation:
Given triangle WXY with sides WX = 7 in and XY = 7 in and angle X = 60°, you want the measure of angle Y and the length of side WY.
Isosceles triangle
The equal given side measures tell you that their opposite angles (W and Y) have equal values. Those values will be such that the total of all angles is 180°:
W +Y +X = 180°
Y +Y +60° = 180° . . . . . . . . . . . use given values; substitute Y for W
Y = (180° -60°)/2 = 60° . . . . . . . subtract 60°, divide by 2
All of the angles in this triangle have the same measure, so it is an equilateral triangle. All of the sides have the same measure, too.
angle Y = 60°
WY = 7 inches
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Additional comment
It is helpful to recognize that an isosceles triangle with a vertex angle of 60° is an equilateral triangle. That recognition lets you write down the answer with no further work.