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mixer
[17]
3 years ago
14
The vertex angle of an isoceles triangle 40 degrees less than the sum of the measures of the base angles. Determine the measure
of the vertex angles.
Mathematics
Answer
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answer:
HACTEHA
[7]
3 years ago
4
0
V = vertex angle
B = base angle
"the vertex angle is 40 degrees less than the sum of the measures of the base angles" means V = B+B-40 which turns into V = 2B-40
Use the fact that the three angles (B, B, V) add up to 180 degrees. Then use substitution to solve for B
V+B+B = 180
V+2B = 180
2B-40+2B = 180
4B-40 = 180
4B = 180+40
4B = 220
B = 220/4
B = 55
Each base angle is 55 degrees
V = 2B-40
V = 2*55-40
V = 110-40
V = 70
The vertex angle is 70 degrees
Check:
V+B+B = 70+55+55 = 180
answer checks out
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