Question

solve the geometry problem.
given the following triangle, find the measure of each angle.
$x - 20^{circ}=

$$square^{circ}$ $x + 10^{circ}=$$

square^{circ}$
$90^{circ}$

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x - 20^{\circ})+(x + 10^{\circ})+90^{\circ}=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x+x)+(-20 + 10+90)=180\), which is \(2x+80 = 180\).

Step3: Solve for \(x\)

Subtract \(80\) from both sides: \(2x=180 - 80\), so \(2x = 100\). Then divide both sides by \(2\): \(x=\frac{100}{2}=50\).

Step4: Find the measure of \(x - 20^{\circ}\)

Substitute \(x = 50\) into \(x-20^{\circ}\): \(50^{\circ}-20^{\circ}=30^{\circ}\).

Step5: Find the measure of \(x + 10^{\circ}\)

Substitute \(x = 50\) into \(x + 10^{\circ}\): \(50^{\circ}+10^{\circ}=60^{\circ}\).

Answer:

\(x - 20^{\circ}=30^{\circ}\), \(x + 10^{\circ}=60^{\circ}\)