Question

Euclid Street is parallel to Lambert Street. City Hall is

located between the streets. From City Hall, a straight
road leads to Euclid Street, intersecting it at a 51°
angle. Another straight road leads to Lambert Street,
intersecting it at a 37° angle. Find X. EXPLAIN and
show your method.

Answer 1

88

Explanation:

Imagine a line through City Hall parallel to the given streets. The angle between that and the path to Euclid Street is 51°, congruent with the alternate interior angle marked 51°.

The angle between our imaginary line and the path to Lambert Street is 37°, congruent with the alternate interior angle marked 37°.

The value of x° is the sum of those two angles:

x° = 51° +37°

x = 88

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Alternate solution

If you extend the path to Euclid Street until it intersects Lambert Street, the alternate interior angle theorem tells you the angle it makes with Lambert Street is 51°. The angle x° is an external angle to the triangle that now has 51° and 37° as remote interior angles. As such, x is the sum of 51 and 37:

x = 51 +37 = 88