   Chapter 2.CT, Problem 12CT ### 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 the figure shown, suppose that A B ¯ ∥ D C ¯ and A D ¯ ∥ B C ¯ . If m ∠ 1 = 82 ° and m ∠ 4 = 37 ° , find m ∠ C . ______________ To determine

To find:

The value of mC.

Explanation

According to the theorem of triangle the sum of interior angle of any triangle will be 180°.

Given:

The following figure shows the given diagram.

Figure (1)

Given that, AB¯DC¯ and AD¯BC¯. If m1=82° and m4=37°.

Approach:

The line AB¯DC¯, and these line have transversal BD¯ and according to the theorem, the alternate interior angles will be congruent. As shown in the figure, 1 and 2 is between AB¯ and CD¯, indicates these are interior angles and are present on opposite side of the transversal BD¯. Therefore, these angles will be alternate angles and also will be congruent with same value. Since, 2 will be equal to the angle 1.

m2=82°.

The line AD¯BC¯, and these lines have transversal BD¯ and according to the theorem, the alternate interior angles will be congruent

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