9.1 Points, Lines, Planes, and Angles Part 2: Angles

Parts of an Angle An angle is made up of two rays with a common endpoint. – The rays forming the angle are called its sides. – The common endpoint of the rays is the vertex of the angle. – The angle is formed by points on the rays and NO OTHER points. (Point X is NOT a point on the angle; it is in the interior of the angle.) This angle can be named  B,  ABC, or  CBA. – The textbook uses the symbol  for “angle”.

Types of Angles A tool called a protractor can be used to measure angles. You can classify angles according to their measures. Symbol for right angle!

Other Types of Angles When two lines intersect to form right angles, they are called perpendicular lines. – Our sense of vertical and horizontal depends of perpendicularity. When two lines intersect, they form two pairs of vertical angles. – Vertical angles always have equal measures.

Finding Angle Measures Find the measure of each marked angle in the given figure.

 Find the measure of each marked angle in the given figure.

 Find the measure of each marked angle in the figure, given that  ABC is a right angle.

Complementary and Supplementary Angles If the sum of the measures of two angles is 90 , the angles are said to be complementary, and each is called the complement of the other. If two angles have a sum of 180 , they are supplementary, and each is the supplement of the other. If a represents the degree measure of an angle, 90 – a represents the measure of its complement and 180 – a represents the measure of its supplement.

Using Complementary and Supplementary Angles The supplement of an angle measures 10  more than three times its complement. Find the measure of the angle.

 The supplement of an angle measures 25  more than twice its complement. Find the measure of the angle.

Angle Relationships A transversal is a line that intersects two parallel lines (line t). Two angles are corresponding angles if they occupy corresponding positions (1 and 5, 3 and 7, 2 and 6, 4 and 8). – These angles are equal. Two angles are alternate exterior angles if they lie outside the two lines on opposite sides of the transversal (1 and 8, 2 and 7). – These angles are equal. Two angles are alternate interior angles if they lie between the two lines on opposite sides of the transversal (3 and 6, 4 and 5). – These angles are equal. Two angles are same side interior angles if they lie between the two lines on the same side of the transversal (3 and 5, 4 and 6). – These angles are supplementary. t

Finding Angle Measures Find the measure of each marked angle, given that lines m and n are parallel.

 Assume that lines m and n are parallel. Find the measure of each marked angle.