Question

a side of the triangle below has been extended to form an exterior angle of 136°. find the value of x.

Explanation:

Step1: Use the linear - pair relationship

The exterior angle of \(136^{\circ}\) and the interior angle adjacent to it form a linear pair. The sum of angles in a linear pair is \(180^{\circ}\). Let the adjacent interior angle be \(y\). Then \(y + 136^{\circ}=180^{\circ}\), so \(y = 180^{\circ}-136^{\circ}=44^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). In the right - angled triangle (one angle is \(90^{\circ}\)), we know that \(x + y+90^{\circ}=180^{\circ}\). Substitute \(y = 44^{\circ}\) into the equation: \(x+44^{\circ}+90^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Simplify the left - hand side of the equation: \(x+(44^{\circ}+90^{\circ})=x + 134^{\circ}\). Then \(x+134^{\circ}=180^{\circ}\). Subtract \(134^{\circ}\) from both sides: \(x=180^{\circ}-134^{\circ}\).

Answer:

\(x = 46\)