Question

question 1. given the triangle below, find the value of x.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Set up an equation

The exterior angle of the triangle is \(110^{\circ}\), and the two non - adjacent interior angles are \(x + 4\) and \(24^{\circ}\). So, we have the equation \((x + 4)+24=110\).

Step3: Simplify the left - hand side of the equation

Combine like terms: \(x+(4 + 24)=110\), which simplifies to \(x+28 = 110\).

Step4: Solve for x

Subtract 28 from both sides of the equation: \(x=110 - 28\).
\(x = 82\)

Answer:

82