In a parallelogram KLMN, angle K = 3x + 18 degrees and angle L = 5x - 12 degrees. Find the measure of each interior angle.

April 19, 2026Mathematics

ScanSolve AI Answer

April 19, 2026

Answer

$83.25^\circ$

$(5x - 12) + (3x + 18) = 180$ $8x + 6 = 180$ $8x = 180 - 6$ $8x = 174$ $x = \frac{174}{8}$ $x = 21.75$

Step 3: Calculate the size of each interior angle. Substitute $x = 21.75$ into the expressions for $\angle N$ and $\angle M$ . $\angle N = 5x - 12^\circ = 5(21.75) - 12 = 108.75 - 12 = 96.75^\circ$ $\angle M = 3x + 18^\circ = 3(21.75) + 18 = 65.25 + 18 = 83.25^\circ$ In a parallelogram, opposite angles are equal. $\angle K = \angle M = 83.25^\circ$ $\angle L = \angle N = 96.75^\circ$

The interior angles are: $\angle K = 83.25^\circ$ $\angle L = 96.75^\circ$ $\angle M = 83.25^\circ$ $\angle N = 96.75^\circ$

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(5x - 12) + (3x + 18) = 180 8x + 6 = 180 8x = 180 - 6 8x = 174 x = (174)/(8) x = 21.75 Step 3: Calculate the size of each interior angle.

Asked on April 19, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 19, 2026

(5x - 12) + (3x + 18) = 180 8x + 6 = 180 8x = 180 - 6 8x = 174 x = (174)/(8) x = 21.75 Step 3: Calculate the size of each interior angle. Substitute x = 21.75 into the expressions for N and M. N = 5x - 12^ = 5(21.75) - 12 = 108.75 - 12 = 96.75^ M = 3x + 18^ = 3(21.75) + 18 = 65.25 + 18 = 83.25^ In a parallelogram, opposite angles are equal. K = M = 83.25^ L = N = 96.75^ The interior angles are: K = 83.25^ L = 96.75^ M = 83.25^ N = 96.75^ What's next? Send 'em!