Question

1. point d is in the interior of ∠abc, m∠abc = 10x - 7, m∠abd = 6x + 5, and m∠dbc = 36°. what is m∠abd?

Explanation:

Step1: Use the angle - addition postulate

Since \(D\) is in the interior of \(\angle ABC\), we have \(m\angle ABC=m\angle ABD + m\angle DBC\).
Substitute the given expressions: \(10x - 7=(6x + 5)+36\).

Step2: Solve the equation for \(x\)

Simplify the right - hand side of the equation: \(10x-7 = 6x+41\).
Subtract \(6x\) from both sides: \(10x-6x-7=6x - 6x+41\), which gives \(4x-7 = 41\).
Add \(7\) to both sides: \(4x-7 + 7=41 + 7\), so \(4x=48\).
Divide both sides by \(4\): \(x=\frac{48}{4}=12\).

Step3: Find \(m\angle ABD\)

Substitute \(x = 12\) into the expression for \(m\angle ABD\).
\(m\angle ABD=6x + 5\), then \(m\angle ABD=6\times12+5\).
\(m\angle ABD=72 + 5=77^{\circ}\).

Answer:

\(77^{\circ}\)