Question

find the indicated angle measures. 19. (mangle abc = 95^{circ}). find (mangle abd) and (mangle dbc).

Explanation:

Step1: Set up an equation

Since \(m\angle ABC=m\angle ABD + m\angle DBC\), we have \((2x + 23)+(9x-5)=95\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \(2x+9x+23 - 5=95\), which simplifies to \(11x+18 = 95\).

Step3: Solve for \(x\)

Subtract 18 from both sides: \(11x=95 - 18=77\). Then divide both sides by 11, so \(x = 7\).

Step4: Find \(m\angle ABD\)

Substitute \(x = 7\) into the expression for \(m\angle ABD\): \(m\angle ABD=2x + 23=2\times7+23=14 + 23=37^{\circ}\).

Step5: Find \(m\angle DBC\)

Substitute \(x = 7\) into the expression for \(m\angle DBC\): \(m\angle DBC=9x-5=9\times7-5=63 - 5=58^{\circ}\).

Answer:

\(m\angle ABD = 37^{\circ}\), \(m\angle DBC=58^{\circ}\)