   Chapter 3.3, Problem 22E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
1 views

# In concave quadrilateral A B C D , the angle at A measures 40 ° . Δ A B D is isosceles, B C → bisects ∠ A B D , and D C → bisects ∠ A D B . What are the measures of ∠ A B C , ∠ A D C ,and ∠ 1 ?

To determine

To find:

The value of ABC, ADC and 1.

Explanation

The measure of the sum of angles of a triangle is equal to 180°.

Given:

The given figure is,

Figure (1)

And,

A=40°, ΔABD is isosceles triangle, BC¯ bisects ABD and BC¯ bisects ABD.

Calculation:

Equate the sum of angles of a triangle to 180°.

Substitute ABD for ADB and 40° for A in equation (1) in order to find the value of ABD.

40°+2ABD=180°2ABD=180°40°=140°2=70°

So,

BC¯ bisects ABD,

ABC=CBA=12(ABD)... (2)

Substitute 70° for ABD in equation (2) in order to find the value of ABC.

ABC=CBA=12(70°)=35°

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