Question

use the given information to find m∠1. m∠4 = 124°, m∠1=(2x)°, m∠2=(x + 31)°. m∠1=□°

Explanation:

Step1: Use exterior - angle property

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(m\angle4=m\angle1 + m\angle2\).

Step2: Substitute the given angle expressions

Substitute \(m\angle4 = 124^{\circ}\), \(m\angle1=(2x)^{\circ}\), and \(m\angle2=(x + 31)^{\circ}\) into the equation: \(124=2x+(x + 31)\).

Step3: Simplify the right - hand side

Combine like terms: \(124=2x+x + 31\), which simplifies to \(124 = 3x+31\).

Step4: Solve for \(x\)

Subtract 31 from both sides: \(124−31=3x\), so \(93 = 3x\). Then divide both sides by 3: \(x=\frac{93}{3}=31\).

Step5: Find \(m\angle1\)

Since \(m\angle1=(2x)^{\circ}\), substitute \(x = 31\) into the expression for \(m\angle1\). So \(m\angle1=2\times31^{\circ}=62^{\circ}\).

Answer:

\(62\)