Question

1. consider the diagram below.

5a solve for x.

Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two non-adjacent interior angles. So:
$$101^\circ = (2x - 18)^\circ + (x - 16)^\circ$$

Step2: Simplify the right-hand side

Combine like terms:
$$101 = 2x - 18 + x - 16$$
$$101 = 3x - 34$$

Step3: Isolate the term with $x$

Add 34 to both sides:
$$101 + 34 = 3x$$
$$135 = 3x$$

Step4: Solve for $x$

Divide both sides by 3:
$$x = \frac{135}{3}$$

Answer:

$x = 45$