Question

in a triangle, an interior - angle is ((x - 10)^{circ}) and an exterior - angle is ((x + 10)^{circ}). options: (x = 85), (x = 88), (x = 90), (x = 100)

Explanation:

Step1: Apply the exterior - angle property of a triangle

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, $(x + 10)=(x-10)+ \text{third interior angle}$. Since the sum of angles on a straight line is $180^{\circ}$, and the angle adjacent to $(x + 10)^{\circ}$ is $(x-10)^{\circ}$, we know that $(x-10)+(x + 10)=180$.

Step2: Simplify the equation

Combine like terms in the equation $(x-10)+(x + 10)=180$. The $- 10$ and $+10$ cancel out, leaving $2x=180$.

Step3: Solve for x

Divide both sides of the equation $2x = 180$ by 2. We get $x=\frac{180}{2}=90$.

Answer:

$x = 90$