Question

22
part a create an equation and solve for x:
image of angle diagram with 149° and 13x + 5° angles
x = blank
part b find the measure of the unknown angle:
unknown angle = blank degrees.
notes:
*vertical angles are equal/congruent.
*angles that are a linear pair are supplementary.
*supplementary is two angles that add up to 180 degrees.

Explanation:

Step1: Set up the equation

The two angles form a linear pair, so their sum is \( 180^\circ \). Thus, \( 149 + (13x + 5) = 180 \).

Step2: Simplify the equation

Combine like terms: \( 154 + 13x = 180 \).

Step3: Solve for \( x \)

Subtract 154 from both sides: \( 13x = 180 - 154 = 26 \). Then divide by 13: \( x = \frac{26}{13} = 2 \).

Step4: Find the unknown angle (Part B)

Substitute \( x = 2 \) into \( 13x + 5 \): \( 13(2) + 5 = 26 + 5 = 31 \).

Answer:

(Part A):
\( x = 2 \)