Problem 24
Answer: w = 120
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Work Shown:
We have an isosceles triangle. The angles opposite the congruent sides are congruent. These are the base angles each 30 degrees. The missing angle is w. The three angles add to 180
(angle1)+(angle2)+(angle3) = 180
30+30+w = 180
60+w = 180
60+w-60 = 180-60 ... subtract 60 from both sides
w = 120
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Problem 25
Answers:
x = 6.5
y = 5
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Work Shown:
The angle marks are all the same, so the three angles are congruent to one another. We consider this an equiangular triangle. Any equiangular triangle is also equilateral, meaning all three sides are the same length.
So,
2x-5 = 8
2x-5+5 = 8+5 ... add 5 to both sides
2x = 13
2x/2 = 13/2 ... divide both sides by 2
x = 6.5
and also,
y+3 = 8
y+3-3 = 8-3 ... subtract 3 from both sides
y = 5
