Question

question 4 of 10
what is the value of x?
100° 70°
x°
a. 70°
b. 10°
c. 30°
d. 170°

Explanation:

Step1: Recall exterior angle theorem

The exterior angle of a triangle equals the sum of the two non - adjacent interior angles. Let the interior angle adjacent to \(100^{\circ}\) be \(y\), then \(y = 180^{\circ}- 100^{\circ}=80^{\circ}\) (linear pair).

Step2: Use triangle angle sum

The sum of interior angles of a triangle is \(180^{\circ}\). Let the unknown angle be \(x\). So \(x + 70^{\circ}+80^{\circ}=180^{\circ}\).

Step3: Solve for x

Simplify the equation: \(x+150^{\circ}=180^{\circ}\). Subtract \(150^{\circ}\) from both sides: \(x = 180^{\circ}- 150^{\circ}=30^{\circ}\).

Answer:

C. \(30^{\circ}\)