TAILIEUCHUNG - Lecture General mathematics: Lecture 19 - Ms. Fehmida Haroon

In this section we’ll look at the arc length of the curve given by, where we also assume that the curve is traced out exactly once. Just as we did with the tangent lines in polar coordinates we’ll first write the curve in terms of a set of parametric equations. | General Mathematics ADE 101 Unit 3 LECTURE No. 19 Types & Measurements of Angles Today’s Objectives Knowledge Test Angles Angles are measured by the amount of rotation. 360° is the amount of rotation of a ray back onto itself. 45° 90° 10° 150° 360° Angles are classified and named with reference to their degree measure. Measure Name Between 0° and 90° Acute Angle 90° Right Angle Greater than 90° but less than 180° Obtuse Angle 180° Straight Angle Angles An angle is the union of two rays that have a common endpoint. An angle can be named with the letter marking its vertex, and also with three letters: the first letter names a point on the side; the second names the vertex; the third names a point on the other side. Vertex B A C Side Side Angles Protractor A tool called a protractor can be used to measure angles. Intersecting Lines When two lines intersect to form right angles they are called perpendicular. Complementary and supplementary angles Complementary and Supplementary Angles If the sum of the measures of two acute angles is 90°, the angles are said to be complementary, and each is called the complement of the other. For example, 50° and 40° are complementary angles If the sum of the measures of two angles is 180°, the angles are said to be supplementary, and each is called the supplement of the other. For example, 50° and 130° are supplementary angles Example: Finding Angle Measure Find the measure of each marked angle below. (2x + 45)° (x – 15)° Solution 2x + 45 + x – 15 = 180 3x + 30 = 180 3x = 150 x = 50 Evaluating each expression we find that the angles are 35° and 145° . Supplementary angles. Adjacent angles Vertical Angles In the figure below the pair are called vertical angles. are also vertical angles. A C B D E Vertical angles have equal measures. Example: Finding Angle Measure Find the measure of each marked angle below. (3x + 10)° (5x – 10)° Solution 3x + 10 = 5x – 10 2x = 20 x = 10 So each angle is 3(10) + 10 = 40°. Vertical angels are equal. .

• Toán học
• General mathematics
• Lecture General mathematics
• Geometric measurement
• Algebraic thinking
• Mathematical knowledge
• Constant functions
• Number pattern
• Cartesian coordinate system
• Liner equations
• Graph of liner equations
• Linear equation
• Natural numbers