   Chapter 3.CR, Problem 22CR ### 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

# Given: A B ¯ ≅ B C ¯ ∠ D A C ≅ ∠ B C D m ∠ B = 50 ° Find: m ∠ A D C To determine

Explanation

Procedure used:

If two sides of the triangle are equal then the corresponding angles are also equal in the triangle.

The sum of interior angles of the triangle is 180°.

Given:

The triangle ΔABC is shown in the figure below,

Figure (1)

From figure (1),

AB¯BC¯DACBCDmB=50°

Calculation:

Consider the triangle ΔABC,

From the given data,

The side AB¯ is congruent to the side BC¯, then the congruent side have same measures. So,

AB¯=BC¯

Since, the two sides of the triangle are equal then the corresponding angles are also equal in the triangle. Then,

mBAC=mBCA

Since, the angle mDAC is congruent to the angle mBCD, then the congruent side have same measures. So,

mDAC=mBCD (1)

Write the equation to calculate the sum of the triangle.

mBAC+mACB+mB=180° (2)

Substitute 50° for mB and mBCA for mBAC in the equation (2) to calculate the sum of the triangle.

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