In the figure, line L1 is parallel to line L2. If the measure of ∠4 = 144°, what is the measure of ∠6 and why? A. 144°, vertical
angles have the same measure B. 144°, corresponding angles have the same measure C. 36°, same side interior angles are supplementary D. 36°, alternate exterior angles are supplementary
2 answers:
Answer:
The measure of ∠6 is 36°
Option C is correct
Step-by-step explanation:
we have to find the measure of ∠6
Since ∠4 and ∠6 angles formed on the same side interior angles and the same-side interior angles that are formed are supplementary, or add up to 180 degrees.
∴ ∠4+∠6=180°
144°+∠6=180°
∠6=180-144=36°
Hence, the measure of ∠6 is 36°
Therefore option C is correct.
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All the points that are 6 units from (-1, 1) are those on the circle
(x+1)^2 +(y-1)^2 = 36
For y=0, the two points of interest satisfy
(x+1)^2 +1 = 36
(x+1)^2 = 35 . . . . . . subtract 1
x+1 = ±√35
x = -1±√35
The points you seek are (-1-√35, 0) and (-1+√35, 0), about (-6.916, 0) and (4.916, 0).
(x+1)^2 +(y-1)^2 = 36
For y=0, the two points of interest satisfy
(x+1)^2 +1 = 36
(x+1)^2 = 35 . . . . . . subtract 1
x+1 = ±√35
x = -1±√35
The points you seek are (-1-√35, 0) and (-1+√35, 0), about (-6.916, 0) and (4.916, 0).