Angles and Angle Pairs

Measure angles and use relationships between pairs.

Lesson 4 of 44 parts Practice Flashcards

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Angles and Their Measures

Objective: Name an angle and classify its measure.

Two rays with a common endpoint form an angle; the common endpoint is its vertex. Acute angles measure less than 90°, right angles 90°, obtuse angles between 90° and 180°, and straight angles 180°.

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Angles and Their Measures

Objective: Name an angle and classify its measure.

Angle Addition

Objective: Add adjacent parts of an angle.

If ray BD lies inside angle ABC, m∠ABD + m∠DBC = m∠ABC.

Ray BD divides angle ABC into adjacent angles ABD measuring 25 degrees and DBC measuring 40 degrees.

Formulas

$m∠ABD + m∠DBC = m∠ABC$

Worked examples

Try itParts of an angle measure 25° and 40°. Find the whole.Show answer

25° + 40° = 65°.

Complementary and Supplementary Angles

Objective: Find missing measures for complementary and supplementary pairs.

Complementary angle measures sum to 90°. Supplementary angle measures sum to 180°. A linear pair consists of adjacent supplementary angles whose outer sides are opposite rays.

A right angle is divided into adjacent 35 and 55 degree angles. A straight angle is divided into adjacent 120 and 60 degree angles.

Formulas

$a + b = 90° (complementary)$
$a + b = 180° (supplementary)$

Worked examples

Try itAn angle is 35°. Find its complement.Show answer

90° − 35° = 55°.

Vertical Angles

Objective: Use vertical angles to find equal measures.

When two lines intersect, each opposite pair of angles is congruent.

Two intersecting lines create an opposite pair of equal 72 degree angles.

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