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31 votes
31 votes
Lines AB and CD and are parallel. Find the measures of the three angles in triangle ABF15742°FB

User Czyzby
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1 Answer

11 votes
11 votes

To calculate the angles you have to star with the uper triangle FCD

The angle with measure 157º and the inner angle of vertex D are supplementary, this means that their measures add up to 180º

180º = 157º+D

D= 180-157=23º

Now that we know the inner angle of D, we can calculate the angle F

Sum of al inner angles of a triangle is 180º, so

180º= C+D+F

F= 180-42-23

F= 115º

Now you can link angles C and B with a Z shaped line, this indicates that they are alternate angles, these type of angles are congruent, so

C=B=42º

Finally you can calculate A by either applying you knowledge of the summ of the inner angles of the triangle or applying the concept of alternate angles.

Angle A can be linked with a Z shaped line to the iiner angle D, meaning that A=D= 23º

Or you can

180º= A+F+B

180º= A+42+115

180º=23º

Angles

A= 23º

F=115º

B=42º

User Jonathan Carroll
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