Answer:
- x = 20 6/7
- ∠3 = 65 3/7
- ∠8 = 65 3/7
Step-by-step explanation:
You have transversal n crossing parallel lines l and m, creating angles labeled 1–8. Angles 1, 3, 6, 8 are shown as obtuse, and the others are shown as acute. You want values of x and angles, given certain angle expressions.
4.
The acute and obtuse angles are supplementary. Angles 3 and 5 are "consecutive interior angles", so are supplementary.
∠3 +∠5 = 180
(4x -18) +(3x +52) = 180
7x +34 = 180 . . . . . . . . . . collect terms
7x = 146 . . . . . . . . . subtract 34
x = 20 6/7 . . . . divide by 7
The measures of the angles are ...
∠3 = 4x -18 = 4(20 6/7) -18 = 83 3/7 -18 = 65 3/7
∠5 = 3x +52 = 3(20 6/7) +52 = 62 4/7 +52 = 114 4/7
Note that the total of angles 3 and 5 is 180°.
The problem asks for the measure of angle 8. Angle 8 is an alternate interior angle with respect to angle 3, so is congruent.
∠8 = ∠3 = 65 3/7
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Additional comment
Note that the angle values of question 4 make the angles that appear to be obtuse in the diagram actually have measures less than 90°. The figure is not drawn to scale.
