Chapter 3.3, Problem 22E

### Elementary Geometry for College St...

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

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 180Â°.

Given:

The given figure is,

Figure (1)

And,

âˆ A=40Â°, Î”ABD is isosceles triangle, BCÂ¯ bisects âˆ ABD and BCÂ¯ bisects âˆ ABD.

Calculation:

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

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

40Â°+2âˆ ABD=180Â°2âˆ ABD=180Â°âˆ’40Â°=140Â°2=70Â°

So,

BCÂ¯ bisects âˆ ABD,

âˆ ABC=âˆ CBA=12(âˆ ABD)... (2)

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

âˆ ABC=âˆ CBA=12(70Â°)=35Â°

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### 64x8y36

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Evaluate the integral. 15. 10x34x+1x23x+2dx

Single Variable Calculus: Early Transcendentals

#### limx0+(1+x)1/x= a) e b) e c) 1e d) 1e

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### For what values of p does the series converge?

Study Guide for Stewart's Multivariable Calculus, 8th