Problem 7)
The sides 2x+4 and 3x-10 are congruent because they are opposite congruent angles. This is an isosceles triangle. Since they are congruent, they are equal. Let's solve for x.
2x+4 = 3x-10
2x+4-2x = 3x-10-2x
4 = x-10
4+10 = x-10+10
14 = x
x = 14
The answer to problem 7 is x = 14
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Problem 8)
This is a right triangle because of the square angle marker. That angle is 90 degrees. This is also an isosceles triangle because of the similar tick marks on the two upper sides. Because this is an isosceles right triangle, that means the triangle is a 45-45-90 triangle. Two angles are 45 degrees.
So,
2x+3 = 45
2x+3-3 = 45-3
2x = 42
2x/2 = 42/2
x = 21
The final answer to problem 8 is x = 21
