Exercise 8 Page 612

From the diagram, we see that two of the triangles angles are

6 0^{\circ} .

Using the Triangle Sum Theorem, we can write the following equation.

6 0^{\circ} + 6 0^{\circ} + m ∠ M = 18 0^{\circ}

Let's solve this equation.

6 0^{\circ} + 6 0^{\circ} + m ∠ M = 18 0^{\circ}

AddTerms

Add terms

12 0^{\circ} + m ∠ M = 18 0^{\circ}

SubEqn

$LHS - 12 0^{\circ} = RHS - 12 0^{\circ}$

m ∠ M = 6 0^{\circ}

The triangle has three congruent angles which means its equiangular. According to the Corollary to the Converse of the Base Angles Theorem, if a triangle is equiangular, then it is equilateral. This means all of the triangle's sides are

16,

including

x .