Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
1. Section 3.1
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Exercise 63 Page 174

Practice makes perfect
a Consider the given diagram.
As we can see, the triangle has two congruent sides, meaning that it is an isosceles triangle. Therefore, the angles opposite the congruent sides must also be congruent.
By the Triangle Angle Sum Theorem, the sum of the measures of all interior angles in a triangle must add up to 180^(∘). x + x + 82^(∘) = 180^(∘) Let's solve this equation.
x + x + 82^(∘) = 180^(∘)
2x+ 82^(∘) = 180^(∘)
2x = 98^(∘)
x = 49 ^(∘)
b Consider the given diagram.
Like in Part A, the triangle has two congruent sides, making it isosceles. This means that the angles opposite the congruent sides must also be congruent.
By the Triangle Angle Sum Theorem, the sum of the measures of all interior angles in a triangle must add up to 180^(∘). x + 71^(∘) + 71^(∘) = 180^(∘) Let's solve this equation.
x + 71^(∘) + 71^(∘) = 180^(∘)
x + 142^(∘) = 180^(∘)
x = 38^(∘)