Question

solve the geometry problem.
given the following triangle, find the measure of each angle.
2x=

x + 50°=

x - 10°=

Explanation:

Step1: Use the triangle - angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((2x)+(x + 50^{\circ})+(x-10^{\circ})=180^{\circ}\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+x + 50^{\circ}+x-10^{\circ}=(2x+x+x)+(50 - 10)^{\circ}=4x + 40^{\circ}\).
The equation becomes \(4x+40^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

Subtract \(40^{\circ}\) from both sides: \(4x=180^{\circ}-40^{\circ}=140^{\circ}\).
Divide both sides by \(4\): \(x=\frac{140^{\circ}}{4}=35^{\circ}\).

Step4: Find the measure of each angle

• For \(2x\): Substitute \(x = 35^{\circ}\), then \(2x=2\times35^{\circ}=70^{\circ}\).
• For \(x + 50^{\circ}\): Substitute \(x = 35^{\circ}\), then \(x + 50^{\circ}=35^{\circ}+50^{\circ}=85^{\circ}\).
• For \(x-10^{\circ}\): Substitute \(x = 35^{\circ}\), then \(x-10^{\circ}=35^{\circ}-10^{\circ}=25^{\circ}\).

Answer:

\(2x = 70^{\circ}\), \(x + 50^{\circ}=85^{\circ}\), \(x-10^{\circ}=25^{\circ}\)