Core Connections Geometry, 2013
CC
Core Connections Geometry, 2013 View details
Chapter Closure

Exercise 137 Page 525

a Consider the given diagram.
The diagram shows an isosceles triangle. We are asked to find the value of x in the expressions for the base angles, so let's recall the Isosceles Triangle Theorem.

Isosceles Triangle Theorem

If two sides in a triangle are congruent, then the angles opposite them are congruent.

By this theorem, the base angles must have the same measure. Let's equate the given expressions. 4x+9^(∘) = 5x+5^(∘) Now we can solve the equation for x.
4x+9^(∘) = 5x+5^(∘)
9^(∘) = x = 5^(∘)
4^(∘) = x
x = 4^(∘)
b Let's consider the given diagram.

Two lines are intersected by a transversal. Notice that we do not know whether those two lines are parallel or not. Since no other information is given, we cannot determine the value of y.

c We want to find the missing angle of the given triangle.

We can use the Triangle Exterior Angle Theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of its two remote interior angles.

Let's use this theorem to write and solve an equation for the missing variable. 40^(∘) + z = 117^(∘) ⇔ z = 77^(∘)