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The total of this whole angle, which is represented by ∠ABD, measures 64°.

We are given that apart of this angle, ∠CBD measures 30°, so that'd mean that the other part of this angle, ∠ABC, would measure 34°.

This is because both angles ABC and CBD combined would equal a total of 64°.

So we set up the equation;

30 + x = 64

-30       -30

x = 34°, therefore ∠ABC = 34°.

m∠ABC = 34°

Step-by-step explanation:

Given:

m∠ABD = 64°

m∠CBD = 30°

BC is the angle bisector of ∠ABD, which means that an angle is cut in half into two equal pieces. The line divides an angle into two angles.

∠ABC + ∠CBD = ∠ABD

m∠ABC = m∠ABD - m∠CBD

m∠ABC = 64° - 30°

m∠ABC = 34°

hope this helps!! p.s. i really need brainliest :)

addition

step-by-step explanation: