Question

name:

1. solve for the unknown angles.

determine the value of x.
(figure of triangle srt with angle at s: (5x - 8)°, angle at r: 67°, angle at t adjacent to 99° on a straight line)

Explanation:

Step1: Find angle at T in triangle SRT

Angles on a straight line sum to \(180^\circ\), so angle \(\angle STR = 180^\circ - 99^\circ = 81^\circ\).

Step2: Use triangle angle sum property

Sum of angles in a triangle is \(180^\circ\). So, \((5x - 8)^\circ + 67^\circ + 81^\circ = 180^\circ\).
Simplify: \(5x - 8 + 67 + 81 = 180\)
\(5x + 140 = 180\)

Step3: Solve for x

Subtract 140 from both sides: \(5x = 180 - 140 = 40\)
Divide by 5: \(x = \frac{40}{5} = 8\)

Answer:

\(x = 8\)