Question

4. In parallelogram LMNP,

Answer 1

Given:

m∠L = 8x - 41

m∠M = 2x + 1

m∠N = 6x + 3

Let's find the measure of angle P

A paralellogram has equal opposite angles.

Therefore, the opposite angles(L and N) and (P and M) are equal.

Thus, we have:

m∠L = m∠N

8x - 41 = 6x + 3

Let's solve for x:

Add 41 to both sided

8x - 41 + 41 = 6x + 3 + 41

8x = 6x + 44

Subtract 6x from both sides:

8x - 6x = 6x - 6x + 44

2x = 44

Divide both sides by 2:

$\begin{gathered} \frac{2x}{2}=\frac{44}{2} \\ \\ x=22 \end{gathered}$

Thus, we have:

m∠P = m∠M = 2x + 1

m∠P = 2x + 1

Substitute 22 for x in (2x + 1)

m∠P = 2(22) + 1

m∠P = 44 + 1

m∠P = 45°

Therefore, the measure of angle P is 45 degrees.

ANSWER:

m∠P = 45°