Question

use the diagram to find the angle measures of the triangle. recall that the sum of the angle measures of a triangle is 180°.
x° = \square°
(x + 5)° = \square°
5x° = \square°

Explanation:

Step1: Set up the equation

The sum of the angles in a triangle is \(180^\circ\). So we have \(x + (x + 5)+5x=180\).

Step2: Combine like terms

Combine the \(x\) terms: \(x+x + 5x=7x\), so the equation becomes \(7x + 5=180\).

Step3: Solve for \(x\)

Subtract 5 from both sides: \(7x=180 - 5=175\). Then divide by 7: \(x=\frac{175}{7} = 25\).

Step4: Find each angle

• For \(x^\circ\): Substitute \(x = 25\), so \(x^\circ=25^\circ\).
• For \((x + 5)^\circ\): Substitute \(x = 25\), \(25+5 = 30\), so \((x + 5)^\circ=30^\circ\).
• For \(5x^\circ\): Substitute \(x = 25\), \(5\times25 = 125\), so \(5x^\circ=125^\circ\).

Answer:

\(x^\circ=\boxed{25}^\circ\)
\((x + 5)^\circ=\boxed{30}^\circ\)
\(5x^\circ=\boxed{125}^\circ\)