Question

1. given (mangle abd = 79^{circ}), determine the value of (x) and (mangle abc).

(5x + 4)°
(8x - 3)°

Explanation:

Step1: Set up equation for angle ABD

Since \(m\angle ABD=(5x + 4)^{\circ}=79^{\circ}\), we solve for \(x\).
\[5x+4 = 79\]

Step2: Isolate the term with \(x\)

Subtract 4 from both sides of the equation.
\[5x=79 - 4\]
\[5x=75\]

Step3: Solve for \(x\)

Divide both sides by 5.
\[x=\frac{75}{5}=15\]

Step4: Find \(m\angle ABC\)

Substitute \(x = 15\) into the expression for \(m\angle ABC=(8x - 3)^{\circ}\).
\[m\angle ABC=8\times15-3\]
\[m\angle ABC = 120 - 3=117^{\circ}\]

Answer:

\(x = 15\), \(m\angle ABC=117^{\circ}\)