Question

practice relating and calculating the measures of interior and exterior angles of a triangle. what is the value of x? there is a triangle fgh with f and h on a straight line (a transversal with arrows), angle at f is 53°, angle at h is 45°, and angle at g is x° (with a line extending from g forming an angle x°).

Explanation:

Step1: Recall triangle exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In triangle \(FGH\), the angle at \(G\) (the exterior angle \(x^{\circ}\)) is equal to the sum of the interior angles at \(F\) and \(H\).

Step2: Calculate the sum of the two interior angles

The measure of the angle at \(F\) is \(53^{\circ}\) and the measure of the angle at \(H\) is \(45^{\circ}\). So we calculate \(53 + 45\).
\(53+45 = 98\)

Answer:

\(98\)