Before you read

Answer first — the lesson below explains it.

An architect designs two complementary roof angles. If one angle measures $37°$ , what is the other angle?

A
$43°$
B
$53°$
C
$127°$
D
$143°$

Check your answer

Answer:

Before you read

Answer first — the lesson below explains it.

Three support struts meet at a point on a straight bridge beam, creating angles of $x °$ , $2 x °$ , and $60°$ . Find $x$ .

A
30
B
40
C
60
D
80

Check your answer

Answer:

Theory

Types of Angle Pairs

Complementary angles: Two angles that sum to $90°$ .

Supplementary angles: Two angles that sum to $180°$ .

$\alpha + \beta = 180°$ Supplementary angles
$\beta = 180° - \alpha$ Solve for the unknown

Supplementary angles sum to 180°

Vertical angles: Formed by two intersecting lines. They are always equal.

$\angle 1 = \angle 3$ Vertical angles are equal
$\angle 2 = \angle 4$ Vertical angles are equal

Vertical angles formed by intersecting lines are always equal

Linear pair: Two adjacent angles that form a straight line. They are supplementary ( $180°$ ).

Example 1

Two angles are supplementary. One is $3x + 10$ and the other is $2x + 20$ . Find $x$ .

$3x + 10 + 2x + 20 = 180$

$5x + 30 = 180$

$5x = 150$ , $x = 30$

x = 30

Quick check

You just read it. Can you apply it?

Two road construction lines intersect at a point. One of the four angles formed measures $125°$ . What are the measures of the other three angles?

A
$55°, 125°, 55°$
B
$55°, 55°, 55°$
C
$125°, 55°, 125°$
D
$35°, 125°, 35°$

Check your answer

Answer:

Vertical angle: $125°$ . Adjacent (supplementary): $180° - 125° = 55°$ each. So: $55°, 125°, 55°$ .

Strategy

SAT Pro Tip

When you see intersecting lines, immediately mark vertical angles as equal and linear pairs as supplementary. This often gives you enough equations to solve for unknowns.

After reading

Same question as before. What do you say now?

An architect designs two complementary roof angles. If one angle measures $37°$ , what is the other angle?

A
$43°$
B
$53°$
C
$127°$
D
$143°$

Check your answer

Answer:

$90° - 37° = 53°$ .

After reading

Same question as before. What do you say now?

Three support struts meet at a point on a straight bridge beam, creating angles of $x °$ , $2 x °$ , and $60°$ . Find $x$ .

A
30
B
40
C
60
D
80

Check your answer

Answer:

$x + 2 x + 60 = 180$ . $3 x = 120$ . $x = 40$ .

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