Question

7 of the given angle (6x + 7)° (8x - 17)° x = m∠dbc =

Explanation:

Step1: Set up equation

Since vertical angles are equal, we set \(6x + 7=8x - 17\).

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(7 = 2x-17\). Then add 17 to both sides: \(24 = 2x\). Divide by 2, so \(x = 12\).

Step3: Find \(m\angle DBC\)

Substitute \(x = 12\) into the expression for \(\angle DBC\) which is \(8x - 17\). So \(m\angle DBC=8\times12 - 17=96 - 17 = 79^{\circ}\).

Answer:

\(x = 12\)
\(m\angle DBC=79^{\circ}\)