CPM Homework Help : CCG Problem 6-97

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6-97.

For each shape below, use the geometric relationships to solve for the given variable(s). Show all work. Name the geometric relationships you used.

Hint (a):
What is the sum of the angles within a triangle?
Answer (a):
$x=15^\circ$ , Triangle Angle Sum

Hint (b):
What do the tick marks on the sides of the triangles mean?
Answer (b):
$k=5$ , Isosceles triangle

Hint (c):
Extend the parallel sides.
More Help (c):
Parallel lines have same side interior supplementary angles.
Step 1(c):
$\begin{array}{l} w+(4t+13)=180º\\ w+(8t−23)=180º \end{array}$
Step 2(c):
By the Equal Values Method: $w+(8t−23)=w+(4t+13)$
Answer (c):
$\begin{array}{l} w+8(9)-23=180\\ w + 72 - 23 = 180\\ w + 49 = 180\\ w = 131º \end{array}$
$\begin{array}{r} 4t = 36\\ t = 9° \end{array}$
Parallel lines

Hint (d):
Use the Law of Cosines to solve for the unknown side.

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