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