Exercise 12 Page 517

Let's analyze the given rhombus.

Note that angles ∠ APD and ∠ DPC are supplementary. Therefore, the measures of ∠ APD and ∠ DPC add to equal 180. m ∠ APD+ m ∠ DPC = 180 We are given that m ∠ APD =90 and m ∠ DPC = 3x-15. We can substitute these expressions into our equation. 90+3x-15 = 180 Now we can solve this equation for x.

90+3x-15=180

SubTerm

Subtract term

75+3x=180

SubEqn

LHS-75=RHS-75

3x=105

DivEqn

.LHS /3.=.RHS /3.

x=35

We found that x=35.