Question

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

x + 30° =

x - 10° =

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Explanation:

Step1: Use the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(2x+(x + 30)+(x-10)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((2x+x+x)+(30 - 10)=180\), which gives \(4x+20 = 180\).

Step3: Solve for \(x\)

Subtract \(20\) from both sides: \(4x=180 - 20=160\). Then divide both sides by \(4\): \(x=\frac{160}{4}=40\).

Step4: Find the measure of each angle

• For \(2x\): Substitute \(x = 40\) into \(2x\), we get \(2\times40=80^{\circ}\).
• For \(x + 30\): Substitute \(x = 40\) into \(x + 30\), we get \(40+30=70^{\circ}\).
• For \(x - 10\): Substitute \(x = 40\) into \(x - 10\), we get \(40-10=30^{\circ}\).

Answer:

\(2x = 80^{\circ}\), \(x + 30^{\circ}=70^{\circ}\), \(x - 10^{\circ}=30^{\circ}\)