In the figure above, if the angle (not shown) where lines n and p intersect is twice as large as the angle (also not shown) where lines l and m intersect, what is the value of x?
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You have to extend lines n & p to form another triangle, and then extend lines l & m to do the same, and then work with the data and the rules for congruent (I think that’s the word) angles equaling 180 and triangles having a total of 180 degrees and quadrilaterals having 360 degrees.
It’s easier to solve the problem if you extend the lines to see the intersections of lines l & m and lines n & p.
Start with the 110deg angle: the supplementary angle is 70deg. 70deg gives you enough info to determine the complementary angle for the triangle formed by lines l, p, n: 20 deg
So now that you know the angle formed by l & m is 20 deg, then the problem states that the angle between n & p is double that: 40deg.
Now you have enough info to solve for the complementary angle in triangle l, p, n.
X must be 50deg.