Question

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

Explanation:

Step1: Set up the equation

Vertical - angles are equal. So, $6x + 7=8x - 27$.

Step2: Solve for x

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

Step3: Find the measure of ∠DBC

Substitute $x = 17$ into the expression for $\angle DBC$ which is $8x - 27$. So, $\angle DBC=8\times17 - 27=136 - 27 = 109^{\circ}$.

Answer:

E. 109°