Question

solve for x. show all your work.
(a)
(b)

Explanation:

Step1: Use exterior - angle property of a triangle

For part (a), the exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. The exterior angle corresponding to the triangle with angle \(x\) can be found using the properties of parallel lines. The angle supplementary to \(117^{\circ}\) is \(180 - 117=63^{\circ}\).
The exterior angle of the triangle with angle \(x\) is \(63 + 56\) (by the property that when a transversal intersects parallel lines, alternate interior angles are equal and then using the exterior - angle property of a triangle).

Step2: Calculate \(x\)

\(x=63 + 56\)
\(x = 119^{\circ}\)

For part (b), first, find the angle supplementary to \(126^{\circ}\), which is \(180 - 126 = 54^{\circ}\).
Then, using the exterior - angle property of a triangle, the exterior angle of the triangle with angle \(x\) is \(54+34\).
So \(x=54 + 34\)
\(x = 88^{\circ}\)

Answer:

a. \(x = 119^{\circ}\)
b. \(x = 88^{\circ}\)