Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
1. Angles of Triangles
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Exercise 21 Page 236

37^(∘) and 53^(∘)

Practice makes perfect

Let's analyze the given triangle.

As we can see, one of its angles is a right angle. Therefore, it is a right triangle. This allows us to use the Triangle Angle-Sum Theorem, which states that acute angles of a right triangle are complementary. In this case, it means that 11x-2 and 6x+7 add up to 90. (11x-2)+(6x+7)=90 By solving this equation, we can find the value of x.
11x-2+6x+7=90
17x+5=90
17x=85
x=5
Once we know the value of x, we can find the exact values of the acute angles. cc 11x-2& →& 11( 5)-2&→& 53^(∘) 6x+7&→&6( 5)+7&→& 37^(∘)