Question

current skill show answer request help 2 4 x + 85 8 1 3 5 4x + 46 find the measure of angle 1.

Explanation:

Step1: Use the property of corresponding angles

Since the two lines are parallel, \(x + 85=4x+46\) (corresponding angles are equal).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(85 = 3x+46\).
Subtract \(46\) from both sides: \(3x=85 - 46=39\).
Divide both sides by \(3\): \(x = 13\).

Step3: Find the measure of angle \(5\)

Substitute \(x = 13\) into \(x + 85\), angle \(5=x + 85=13+85 = 98^{\circ}\).

Step4: Use the property of supplementary angles

Angle \(1\) and angle \(3\) are supplementary to angle \(5\) (linear - pair). Since angle \(3\) and angle \(5\) are equal (alternate interior angles for parallel lines), angle \(1=180^{\circ}-98^{\circ}=82^{\circ}\).

Answer:

\(82^{\circ}\)