Question

9 multiple choice 1 point solve for x. image of two parallel lines cut by a transversal, with angles x + 90 and x + 110 on one of the parallel lines options: -10, -5, 3, -9

Explanation:

Step1: Identify supplementary angles

The two angles $\boldsymbol{x+90}$ and $\boldsymbol{x+110}$ form a linear pair, so they are supplementary (sum to $180^\circ$).
$$(x + 90) + (x + 110) = 180$$

Step2: Simplify the left side

Combine like terms.
$$2x + 200 = 180$$

Step3: Isolate the variable term

Subtract 200 from both sides.
$$2x = 180 - 200$$
$$2x = -20$$

Step4: Solve for x

Divide both sides by 2.
$$x = \frac{-20}{2}$$
$$x = -10$$

Answer:

-10