Question

find x. then plug x in and find the measure of angle abc. what is the measure of abc? a (6x + 10) b (4x) c 17 112 129 180

Explanation:

Step1: Identify supplementary angles

Angles \( (6x + 10)^\circ \) and \( (4x)^\circ \) are supplementary (form a linear pair), so their sum is \( 180^\circ \).

$$ (6x + 10) + 4x = 180 $$

Step2: Solve for \( x \)

Combine like terms:

$$ 10x + 10 = 180 $$

Subtract 10 from both sides:

$$ 10x = 170 $$

Divide by 10:

$$ x = 17 $$

Step3: Find measure of \( \angle ABC \)

\( \angle ABC \) is \( (6x + 10)^\circ \). Substitute \( x = 17 \):

$$ 6(17) + 10 = 102 + 10 = 112 $$

Answer:

112