Curriculum

Course: Mathematics — First Preparatory

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Curriculum

Mathematics — First Preparatory

Unit 1: Numbers

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Unit 2: Algebra

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Unit 3: Statistics

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Unit 4: Geometry

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Text lesson

Types of Angles and Their Relations

Mathematics — First Preparatory

Types of Angles and Their Relations

Worked examples

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Find the complement of 35°	Findcomplement
Solution	The complement = 90 − 35 = 55°	complement
Example 2	Find the supplement of 115°	Findsupplement
Solution	The supplement = 180 − 115 = 65°	supplement
Example 3	Two vertically opposite angles measure 2x + 10 and x + 40. Find x and the measure of each angle	verticallyoppositeanglesmeasure
Solution	Vertically opposite angles are equal so 2x + 10 = x + 40 which gives x = 30. The angle measures 2 × 30 + 10 = 70°	Verticallyoppositeanglesequal
Example 4	Two adjacent angles lie on a straight line. One measures x and the other measures 2x. Find both measures	adjacentanglesstraightline
Solution	Their sum is 180 so 3x = 180 and x = 60. The two angles measure 60° and 120°	anglesmeasure
Example 5 (the hardest)	Two parallel lines are cut by a transversal. The alternate angles measure 4x − 20 and 2x + 40. Find the angle	parallellinestransversalalternate

Solution→Alternate angles are equal, so 4x − 20 = 2x + 40, which gives 2x = 60 and x = 30. The angle measures 4 × 30 − 20 = 100°. Check: 2 × 30 + 40 = 100.

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