   Chapter 7.2, Problem 39E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Δ A B C , the bisectors of the angle are concurrent at point D . If m ∠ C A B = 64 ∘ and m ∠ A B C = 82 ∘ , find m ∠ E D C . Exercises 39, 40

To determine

To find:

The angle mEDC in triangle ABC.

Explanation

Definition:

Angle bisector of a triangle:

The angle bisector of a triangle is a line segment that bisects one of the vertex angles of a triangle.

In general an angle bisector is equidistant from the sides of the angle when measured along a segment perpendicular to the sides of the angle.

Given:

In ΔABC, the bisectors of the angle are concurrent at point D. If mCAB=64 and mABC=82.

Clarification:

The sum of measures of three angles of any triangle is equal to 180.

By the given triangle ABC,

mCAB+mABC+mBCA=18064+82+mBCA=180Subtracting64and82onbothsides,64+82+mBCA6482=1806482mBCA=34

Next we consider the triangle ECB,

In above figure BE bisects the B vertex angles of a triangle.

And also mBCA=mECB=34.

mECB+mCBE+mBEC=18034+B2+mBEC=18034+822+mBEC=18034+41+mBEC=180Subtracting34and41onbothsides,

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