LA and ZB are supplementary. If the mZB is 49°, what is the m/A?What type of reasoning do you use, inductive or deductive, whensolving this problem? Explain.

Answered: LA and ZB are supplementary. If the mZB…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter3: Triangles

Section3.1: Congruent Triangles

Problem 7E: In ABC, the midpoints of the sides are joined. a what does intuition suggest regarding the...

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LA and ZB are supplementary. If the mZB is 49°, what is the m/A?
What type of reasoning do you use, inductive or deductive, when
solving this problem? Explain.

Expert Solution

Step 1

Given: $∠ A$ and $∠ B$ are supplementary and $m ∠ B = 49 °$ .

To find: $m ∠ A$ .

Solution:

We know that two angles are called supplementary if their sum is equal to $180 °$ .

We have given that $∠ A$ and $∠ B$ are supplementary.

Therefore,

$\begin{array}{rcl} m ∠ A + m ∠ B & = & 180 ° \\ m ∠ A + 49 ° & = & 180 ° [Given m ∠ B = 49 °] \\ m ∠ A & = & 180 ° - 49 ° \\ m ∠ A & = & 131 ° \end{array}$

Therefore, $m ∠ A = 131 °$ .

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LA and ZB are supplementary. If the mZB is 49°, what is the m/A? What type of reasoning do you use, inductive or deductive, when solving this problem? Explain.