Question

in the figure above, two parallel lines, m and n, are cut by transversal t. given that (mangle2=(2x + 7)^{circ}) and (mangle7=(3x - 13)^{circ}). what is the (mangle5?
20^{circ}
47^{circ}
73^{circ}
133^{circ})

Explanation:

Step1: Use the property of alternate - exterior angles

Since lines \(m\) and \(n\) are parallel and \(t\) is a transversal, \(\angle2\) and \(\angle7\) are alternate - exterior angles. Alternate - exterior angles are congruent, so \(m\angle2=m\angle7\).

$$2x + 7=3x-13$$

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides of the equation:

$$7=x - 13$$

Then add 13 to both sides:

$$x=7 + 13=20$$

Step3: Find the measure of \(\angle7\)

Substitute \(x = 20\) into the expression for \(m\angle7\):

$$m\angle7=(3x-13)^{\circ}=(3\times20 - 13)^{\circ}=(60 - 13)^{\circ}=47^{\circ}$$

Step4: Use the property of vertical angles

\(\angle5\) and \(\angle7\) are vertical angles. Vertical angles are congruent, so \(m\angle5=m\angle7 = 47^{\circ}\)

Answer:

47°