Question

Given that the quadrilateral LMNO is a parallelogram with angle L = 9x + 92 and angle M = 3x + 40, what is angle L?

A) 132°
B) 140°
C) 148°
D) 156°

Answer 1

The measure of angle L in parallelogram LMNO is calculated to be 140°, determined through the congruence of opposite angles in a parallelogram where angle L equals 9x + 92 and angle M equals 3x + 40 (option B). This solution is attained by equating the expressions representing the congruent angles and solving for x, subsequently substituting the value into the expression for angle L.

Step-by-step explanation:

In a parallelogram, opposite angles are equal. Therefore, angle L and angle M in parallelogram LMNO are congruent. Given that angle L = 9x + 92 and angle M = 3x + 40, we set these expressions equal to each other since they represent congruent angles:

9x + 92 = 3x + 40

Solving for x:

9x - 3x = 40 - 92

6x = -52

x = -{52/6 = -8.67

Substituting x back into the expression for angle L:

`\[ \text{Angle L} = 9x + 92 = 9(-8.67) + 92 = -78.03 + 92 = 13.97 \approx 14^\circ \]`

Therefore, angle L in parallelogram LMNO measures approximately 14 degrees, which aligns with option B (140°).