Nicole W.

asked • 01/23/21# Please help me ASAP!

Given: ∠ABD≅∠BDE

prove: ∠CBD≅∠CDB. C

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/ \ Note: AC and CE are segments

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B /________\ D

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A / \ E

## 2 Answers By Expert Tutors

CBD = 180º - ABD = 180º - BDE = CDB

Dear Nicole,

How did you include that diagram? That worked awesome! I want to be able to do that!

The key to solving this problem is to consider the **meaning of supplemental angles**. They are pairs of angles that, when laid side to side, form a straight line with their outer rays. That's an awkward way of saying it. Mathematically, they are two angles whose measures add to 180 degrees, which is the measure of a straight line.

Given: ∠ABD≅∠BDE

prove: ∠CBD≅∠CDB

m∠ABD + m∠CBD = 180 Definition of supplementary angles

m∠BDE + m∠CDB = 180 Definition of supplementary angles

m∠CBD = 180 – m∠ABD Algebraic manipulation of above equation

m∠CDB = 180 – m∠BDE Algebraic manipulation of above equation

m∠CBD = 180 – m∠BDE Substitution of equivalents

m∠CBD = m∠CDB Substitution of equivalents

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James M.

01/23/21