Answers:
- problem 6) x = 5
- problem 7) x = 5
- problem 8) x = 4
- problem 9) x = 6
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Step-by-step explanation:
The angles with the similar arc markers are congruent angles. This is only when we consider any particular triangle isolated from the others.
Since we have 2 congruent angles, the triangles are considered isosceles. The congruent sides are opposite the congruent angles.
So we'll set the congruent side expressions equal to one another and solve for x. We ignore the side that isn't opposite one of the congruent angles. This applies to all four problems.
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Work Shown for Problem 6:
3x = x+10
3x-x = 10
2x = 10
x = 10/2
x = 5
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Work Shown for Problem 7:
x = 10-x
x+x = 10
2x = 10
x = 10/2
x = 5
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Work Shown for Problem 8:
4x-12 = x
4x-x = 12
3x = 12
x = 12/3
x = 4
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Work Shown for Problem 9:
2(x+3) = 18
2x+6 = 18
2x = 18-6
2x = 12
x = 12/2
x = 6
Or you can solve it like this
2(x+3) = 18
x+3 = 18/2
x+3 = 9
x = 9-3
x = 6