Question

what is the value of x? diagram: triangle fgh with point f on a line (two arrows), point h on a line (one arrow), angle at f is 53°, angle at h is 45°, angle at g is ( x^circ )

Explanation:

Step1: Find the third angle in triangle FGH

The sum of angles in a triangle is \(180^\circ\). So the third angle at \(G\) (inside the triangle) is \(180^\circ - 53^\circ - 45^\circ\).
\[180 - 53 - 45 = 82^\circ\]

Step2: Find \(x\) using linear pair

\(x\) and the \(82^\circ\) angle form a linear pair (they are supplementary, sum to \(180^\circ\)). So \(x = 180^\circ - 82^\circ\).
\[x = 98^\circ\]

Answer:

\(98\)