Exercise 122 Page 66

By the Triangle Angle Sum Theorem, we know that the triangle's angles should sum to 180^(∘). m∠ A+m∠ B+m∠ C=180^(∘) To determine these angles, we have to translate the verbal description of angle ∠ A in terms of ∠ B into equations. The measure of angle $A$ is $5^(∘)$ more than 3 times the measure of angle $B$ m∠ A = 3m∠ B + 5^(∘) We will also translate the description of angle C. angle $C$ measures $20^(∘)$ less than angle $B$ m∠ C = m∠ B - 20^(∘) Since we have equations for ∠ A and ∠ C in terms of ∠ B, we can substitute this into our first equation and solve for m∠ B.

Having found that m∠ B= 39^(∘), we can find the measures of ∠ A and ∠ B using the equations we wrote earlier. m∠ A&= 3( 39^(∘))+5^(∘)=122^(∘) m∠ C&= 39^(∘)-20^(∘) = 19^(∘)