Question

Jeremy is designing a graphic for his business. The graphic is a banner in the shape of a parallelogram, MHWP , as shown.

If angle M=(22x+19) and angle H (15x+13) , find the measure of each angle in the parallelogram.

Answer 1

The missing angles are;

∠M = 107°

∠H = 73°

∠W = 107°

∠P = 73°

How to find the angles in a Parallelogram?

We know that opposite angles of a parallelogram are equal (or congruent). We also know that consecutive angles of a parallelogram are supplementary angles to each other.

Thus;

∠M + ∠H = 180°

We are given:

∠M = 22x + 19

∠H = 15x + 13

Thus;

22x + 19 + 15x + 13 = 180

37x + 32 = 180

37x = 180 - 32

37x = 148

x = 4

Thus:

∠M = 22(4) + 19 = 107°

∠H = 15(4) + 13 = 73°

Since opposite angles are congruent, then we have;

∠W = 107°

∠P = 73°