Question

15 - 20. find x:
15.
16.

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.
For problem 15:
The exterior angle \(x^{\circ}\) is equal to the sum of the angles \(28^{\circ}\) and \(37^{\circ}\).
So, \(x = 28+37\)

Step2: Calculate the value of \(x\)

\(x=65\)

For problem 16:
The exterior angle \(3x + 8\) is equal to the sum of the two non - adjacent interior angles \(\frac{3}{2}x\) and \(\frac{5}{3}x\)
First, find a common denominator for \(\frac{3}{2}x+\frac{5}{3}x\). The common denominator of 2 and 3 is 6.
\(\frac{3}{2}x+\frac{5}{3}x=\frac{3\times3}{2\times3}x+\frac{5\times2}{3\times2}x=\frac{9}{6}x+\frac{10}{6}x=\frac{9 + 10}{6}x=\frac{19}{6}x\)
Set up the equation: \(\frac{19}{6}x=3x + 8\)
Multiply through by 6 to clear the fraction: \(19x=18x + 48\)
Subtract \(18x\) from both sides: \(19x-18x=18x + 48-18x\)
\(x = 48\)

Answer:

1. \(x = 65\)
2. \(x = 48\)