PLEASE HELP THE SEMESTER IS ENDING IN 2 WEEKS AND IF I DONT COMPLETE THIS IM GOING TO FAIL ;(( ILL MARK BRAINLIEST

Mathematics

1 answer:

EleoNora [17]1 year ago

6 0

The angles m∠ABC = (3·x - 2)° and m∠ABD formed by the ray $\overrightarrow{BA}$ , which is an angle bisector of angle m∠CBD = (5·x + 18)°, indicates that m∠ABD is 64°

<h3>What is an angle bisector?</h3>

An angle bisector is a line, segment or ray that divides an angle into two congruent angles.

The information in the question are;

The ray that bisects ∠CBD = $\overrightarrow{BA}$

The measure of angle, m∠CBD = (5·x + 18)°

The measure of angle, m∠ABC = (3·x - 2)°

Therefore;

(5·x + 18)° = 2 × (3·x - 2)° (definition of angle formed by an angle bisector)

(5·x + 18)° = (6·x - 4)°

(6·x - 5·x)° = (18 + 4)°

x = 22°

m∠CBD = m∠ABD + m∠ABC (angle addition postulate)

m∠ABD = m∠ABC (angles formed by angle bisector $\overrightarrow{BA}$ )

m∠ABC = (3·x - 2)°

Therefore; m∠ABC = (3 × 22 - 2)° = 64°

m∠ABD = m∠ABC = 64°

Learn more about the angle addition postulate here:

brainly.com/question/4208193

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