Geometry) Based on the information provided, what is the measure of ∠CBD ? m∠CBD =__________.

Question

Use the figure to answer the question. 

Based on the information provided, what is the measure of ∠CBD ?

m∠CBD =__________.

Enter the number that belongs in the blank in the previous sentence, like this: 42

Answer 1

The key is to notice that you see

-- a triangle (180 degrees = interior angles) and

-- a line (180 degrees along a line).

First, the triangle:

43 + 89 + ABC = 180 ---- because the interior angles of a triangle sum to 180 degrees

ABC = 180 - (43 + 89) ---- rewritten

ABC = 48

Next, the line:

ABC + CBD = 180 ---- because ABC and CBD are supplementary (on a line, sum to 180 degrees)

CBD = 180 - ABC

CBD = 180 - 48 ---- substituting the value 48 for what you found for ABC in the triangle, above

CBD = 132

Or, you could combine those insights and see that 43+89 = the supplement to ABC, therefore, you don't need ABC to solve this problem. By the transitive property, you can see that

-- the supplement to ABC is 43 + 89

-- the supplement to ABC is CBD

-- therefore 43 + 89 = CBD

CBD = 43 + 89

CBD = 132

Let me know if you have any questions, and I'll be glad to help!

Lindsey

Answer 2

Hi Klauss,

By External Angle Theorem (Triangle),

<CBD = 43 + 89 = 132

Please let me know if you need further help.

Katherine