The measures of the angles D, F and B are 43°, 105° and 32°, respectively. (Correct choice: C)
What are the values of the missing angles?
Herein we find a geometric system generated by two parallel lines and two lines that pass through the two lines. The values of the missing angles by using triangle properties and concepts of alternating internal angles, supplementary angles and vertical angles. Now we proceed to find the measures of the missing angles:
- m ∠ C + m ∠ F + m ∠ D = 180° Sum of the measures of internal angles in a triangle
- m ∠ D = 180° - 137° = 43° Supplementary angles
- m ∠ F = 180° - 32° - 43° = 105° Step 1 / Algebra
- m ∠ F' = 105° Step 3 / Vertical angles
- m ∠ B = m ∠ C = 32° Internal alternating angles
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