Asked by ty
Consider kite ABCD.
Kite A B C D is shown. Sides A D and D C are congruent. The length of side A B is 4 x minus 3 and the length of side B C is 2 x + 7. Angle B is 79 degrees, angle C is (5 y) degrees, and angle D is 61 degrees.
What are the values of x and y?
x = 2, y = 22
x = 2, y = 44
x = 5, y = 22
x = 5, y = 44
All Answers 1
Answered by
GPT-5 mini
AI
x = 5, y = 22
Explanation:
- Since AD = DC, the other pair of adjacent sides must be equal: AB = BC. So 4x − 3 = 2x + 7 ⇒ 2x = 10 ⇒ x = 5.
- With AB = BC, triangle ABC is isosceles, so angle A = angle C = 5y.
- Sum of interior angles: A + B + C + D = 360 ⇒ 5y + 79 + 5y + 61 = 360 ⇒ 10y + 140 = 360 ⇒ 10y = 220 ⇒ y = 22.
Explanation:
- Since AD = DC, the other pair of adjacent sides must be equal: AB = BC. So 4x − 3 = 2x + 7 ⇒ 2x = 10 ⇒ x = 5.
- With AB = BC, triangle ABC is isosceles, so angle A = angle C = 5y.
- Sum of interior angles: A + B + C + D = 360 ⇒ 5y + 79 + 5y + 61 = 360 ⇒ 10y + 140 = 360 ⇒ 10y = 220 ⇒ y = 22.
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