Exercise 54 Page 146

Angles ∠ YDF and ∠ YDA are supplementary angles.

m∠ YDA = 59^(∘)

Practice makes perfect

We are given that m∠ YDF=121^(∘). Let's note this information on the diagram.

Now, since ∠ YDF and ∠ YDA form a linear pair we can say that ∠ YDF and ∠ YDA are supplementary angles. Therefore, their measures add to equal 180 ^(∘). m∠ YDF + m∠ YDA = 180^(∘) By substituting 121^(∘) for m∠ YDF into the equation, we can solve for the measure of ∠ YDA.

m∠ YDF + m∠ YDA = 180^(∘)

Substitute

∠ YDF= 121^(∘)

121^(∘) + m∠ YDA = 180^(∘)

SubEqn

LHS-121^(∘)=RHS-121^(∘)

m∠ YDA = 180^(∘)-121^(∘)

SubTerm

Subtract term

m∠ YDA = 59^(∘)

We found that the measure of ∠ YDA is 59^(∘).