Question

the measures of the angles of a triangle are shown in the figure below. solve for x. 45° 75° x°

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(45^\circ + 75^\circ + x^\circ = 180^\circ\).

Step2: Calculate sum of known angles

Add \(45^\circ\) and \(75^\circ\): \(45 + 75 = 120\). So, \(120^\circ + x^\circ = 180^\circ\).

Step3: Solve for \(x\)

Subtract \(120^\circ\) from both sides: \(x = 180 - 120 = 60\).

Answer:

\(x = 60\)