Question

question 8
2 points
find the measure of angle m based on the shape below.
quadrilateral klmn with angle k = 97°, angle n = (30x - 2)°, angle m = (31x + 3)°, angle l = (25x + 4)°
options: 88°, 79°, 96°, 3°

Explanation:

Step1: Sum of quadrilateral angles

The sum of interior angles of a quadrilateral is $360^\circ$. So:
$$97 + (25x + 4) + (31x + 3) + (30x - 2) = 360$$

Step2: Simplify the equation

Combine like terms:
$$97 + 4 + 3 - 2 + 25x + 31x + 30x = 360$$
$$102 + 86x = 360$$

Step3: Solve for $x$

Isolate the variable term:
$$86x = 360 - 102$$
$$86x = 258$$
$$x = \frac{258}{86} = 3$$

Step4: Calculate angle M

Substitute $x=3$ into $(31x + 3)$:
$$31(3) + 3 = 93 + 3 = 96$$

Answer:

96° (Option C: 96°)