Question

1 find m∠dbc. a (6x + 7)° e b d (8x - 27)° c a) 95° mrs. healy b) 98° mr. addison c) 102° ms. fitzgerald d) 105° mr. jacobs e) 109° mrs. steele © gina wilson (all things algebra), 2014

Explanation:

Step1: Set up equation

Since vertical angles are equal, we set $6x + 7=8x - 27$.

Step2: Solve for x

Subtract $6x$ from both sides: $7 = 2x-27$. Then add 27 to both sides: $34 = 2x$. Divide by 2, so $x = 17$.

Step3: Find angle measure

Substitute $x = 17$ into $6x + 7$. We get $6\times17+7=102 + 7=109$.

Answer:

E. 109°