Question

diagram with two parallel horizontal lines, a transversal forming 117° with the top line, another transversal forming 56° with the top line, and a triangle with angle x° (to find x).

Explanation:

Step1: Find the supplementary angle

The angle adjacent to \(117^\circ\) on a straight line is supplementary, so it is \(180^\circ - 117^\circ = 63^\circ\).

Step2: Use the triangle angle - sum property

In a triangle, the sum of angles is \(180^\circ\). We know one angle is \(63^\circ\) (from step 1) and another angle is equal to \(56^\circ\) (corresponding angles, since the lines are parallel). Let the third angle be \(x\). Then \(x+63^\circ + 56^\circ=180^\circ\).

Step3: Solve for \(x\)

First, calculate the sum of the known angles: \(63^\circ+56^\circ = 119^\circ\). Then, \(x=180^\circ - 119^\circ=61^\circ\).

Answer:

\(x = 61\)