Exercise 11 Page 305

Notice that ∠ 9 and ∠ 10 form a linear pair.

The Supplement Theorem tells us that they are supplementary angles, and we get the following relation. m∠ 9+m∠ 10 = 180 Now, let's substitute m∠ 9= 3x+12 and m∠ 10= x-24 into this equation and solve for x.

Finally, we find the measures of ∠ 9 and ∠ 10 by substituting x=48 into their expressions. lll m∠ 9=3x+12 & ⇒ & m∠ 9=3( 48)+12 & & =156 m∠ 10=x-24 & ⇒ & m∠ 10= 48-24 & & =24