Question

fill in the blank 1 point
9.

m∠j = type your answer...°
m∠k = type your answer...°
m∠l = type your answer...°
m∠m = type your answer...°

Explanation:

Step1: Identify same-side interior angles

In trapezoid \(JKLM\) with \(JK \parallel ML\), \(\angle J\) and \(\angle L\) are same-side interior angles, so they are supplementary:
$$(7x + 2) + (25x - 14) = 180$$

Step2: Solve for \(x\)

Combine like terms and isolate \(x\):
$$32x - 12 = 180$$
$$32x = 192$$
$$x = \frac{192}{32} = 6$$

Step3: Calculate \(m\angle J\)

Substitute \(x=6\) into \(\angle J\)'s expression:
$$m\angle J = 7(6) + 2 = 42 + 2 = 44$$

Step4: Calculate \(m\angle L\)

Substitute \(x=6\) into \(\angle L\)'s expression:
$$m\angle L = 25(6) - 14 = 150 - 14 = 136$$

Step5: Calculate \(m\angle K\)

\(JKLM\) is an isosceles trapezoid (marked sides \(JL=KM\)), so base angles are equal:
$$m\angle K = m\angle J = 44$$

Step6: Calculate \(m\angle M\)

In an isosceles trapezoid, the other pair of base angles are equal:
$$m\angle M = m\angle L = 136$$

Answer:

\(m\angle J = 44^\circ\)
\(m\angle K = 44^\circ\)
\(m\angle L = 136^\circ\)
\(m\angle M = 136^\circ\)