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Work out the size of angle x.

Work out the size of angle x.-example-1
User Sectechguy
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Explanation:

remember, the sum of all angles in a triangle is always 180°.

and the angles at an intersection of a line with parallel lines are the same for each parallel line.

also, the angles on both side of an intersected line are the same, but left-right mirrored.

and, the sum of all angles around a single point on one side of a line is also always 180° (because that line would be the diameter of a circle with that point as its center, so each side of the line represents a half-circle with 180°).

let's consider the top most triangle.

the top angle is x.

the bottom left inner angle is 85° (the same angle as on the other side of the intersected line).

the bottom right inner angle is 180 - 98 = 82° (because the outer angle is also 98°, and then the inner angle is the supplement of 98 to 180).

and so,

180 = x + 85 + 82

x = 180 - 167 = 13°

User Jazmen
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