Question

find the measure of the angle indicated. (equation required)

1. find ( mangle tbc ).

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.
So, \(13x + 8=6x + 57\)

Step2: Solve the equation for \(x\)

Subtract \(6x\) from both sides:
\(13x-6x + 8=6x-6x + 57\)
\(7x+8 = 57\)
Subtract \(8\) from both sides:
\(7x+8 - 8=57 - 8\)
\(7x=49\)
Divide both sides by \(7\):
\(x=\frac{49}{7}=7\)

Step3: Find the measure of \(\angle TBC\)

Substitute \(x = 7\) into \(13x + 8\)
\(m\angle TBC=13\times7+8\)
\(=91 + 8\)
\(=99^{\circ}\)

Answer:

\(m\angle TBC = 99^{\circ}\)