Triangle ๐ฟ๐ ๐ is isosceles with ๐ฟ๐ = ๐ฟ๐.What is the value of ๐ฆ?A 15 B 17 C 19 D 21 E 23๐ ๐๐ฟ(2๐ฅ +8)โฆ (3๐ฅ โ20)โฆ(4๐ฆโ8)โฆ
Question
Triangle ๐ฟ๐ ๐ is isosceles with ๐ฟ๐ = ๐ฟ๐.
What is the value of ๐ฆ?
A 15
B 17
C 19
D 21
E 23
๐
๐
๐ฟ
(2๐ฅ +8)โฆ
(3๐ฅ โ20)โฆ
(4๐ฆโ8)โฆ
Solution
To solve for y, we need to know that the sum of the angles in a triangle is 180 degrees.
Since the triangle is isosceles, the base angles are equal. Therefore, we can set the expressions for the base angles equal to each other:
2x + 8 = 3x - 20
Solving for x gives:
x = 28
Substitute x = 28 into the expression for the vertex angle:
4y - 8 = 180 - [(2(28) + 8) + (3(28) - 20)]
Solving for y gives:
4y = 104 + 8
4y = 112
y = 112 / 4
y = 28
However, this is not an option in the given choices. There seems to be a mistake in the problem or the options.
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