Question

In a city, 6th and 7th Avenues are parallel and the corner that The Pizza Palace is on is a 54° angle. What is the measure of the angle that is made with 7th Ave and Broadway on the corner of The Shake Hut?

Answer 1

Denote

$a_6$ - 6th Avenue,

$a_7$ - 7th Avenue,

P - The Pizza Palace and S - The Shake Hut.

Therefore, you have two parallel lines $a_6$, $a_7$ and transversal PS. Given m∠P=54°, you have to find m∠S. Angles are consecutive interior angles with property

m∠P+m∠S=180°.

Then m∠S=180°-54°=126°.

Answer: 126°

Answer 2

The measure of the angle that is made with 7th Ave and Broadway on the corner of The Shake Hut is 126°.

Equation

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the angle opposite the Pizza palace, hence:

x = 54° (vertical opposite angles are equal)

Also:

The snake hut + x = 180 (consecutive angles are supplementary)

The snake hut + 54 = 180

The snake hut = 126°

The measure of the angle that is made with 7th Ave and Broadway on the corner of The Shake Hut is 126°.

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