Answer:
(b) 61.3°
Explanation:
You want the measure of angle 20 in the diagram with parallel lines creating angle 6 = 3x -5, angle 19 = 6x -14, and angle 20 congruent to angle 6 and supplementary to angle 19.
Angle relations
Angles 6 and 20 are alternate interior angles, so are congruent. Angles 19 and 20 are a linear pair, so are supplementary. This tells us ...
∠6 + ∠19 = 180°
(3x -5) +(6x -14) = 180
9x -19 = 180
9x = 199
x = 22 1/9
Now, we can find the measures of angle 6 and 20.
∠20 = ∠6 = 3(22 1/9) -5 = 66 1/3 -5
∠20 = 61 1/3° ≈ 61.3°
The measure of angle 20 is about 61.3°.
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Additional comment
We can use z = 3x-5 as the measure of angle 6 (and angle 20). Writing angle 19 in terms of this, we have ...
∠19 = 6x -14 = 2(3x -5) -4 = 2z -4
Now, the equation for the supplementary angles is ...
z +(2z -4) = 180
3z = 184
z = 61 1/3 . . . . . . . . the measures of angles 6 and 20
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