Finding Angle Measures
The straight lines OA and OB meet at the point ‘O’, which is called the vertex of the angle AOB. OA and OB are the arms of the angle AOB. The amount of turning from OA to OB is called the measure of ÐAOB. The measure of ÐAOB does not depend upon the length of arms OA, OB of the angle.
If the straight line segment OA rotates about ‘O’ through a complete rotation then it will come back to its own position. This complete rotation is divided into 360 equal parts. Each part is called a degree and it is denoted by ‘°’. The measure of half the rotation is 180°.
One fourth the rotation will have a measure of 90°, which is called a ‘right angle’.
An angle with a measure less than 90° is called an ‘acute’ angle.
An angle with its measure lying between 90° and 180° is called an ‘obtuse’ angle.
An angle with its measure lying between 180° and 360° is called a ‘reflex’ angle.
Two angles which have a common vertex and have a common arm are called ‘adjacent’ angles.
∠ AOB and ∠ BOC are adjacent angles with OB as the common arm.
Example: If ∠AOB = 90°, find the value of ∠AOE, ∠EOD and ∠DOB.
∠AOE + ∠EOD + ∠DOB = 90° (Given ∠AOB = 90°)
(2x – 3) + (2x + 4) + (x + 9) = 90°
5x + 10 = 90
5x = 80 => x = 16
So, ∠AOE = 2x – 3 = (2 × 16) – 3 = 32 – 3 = 29°
∠EOD = 2x + 4 = (2 × 16) + 4 = 32 + 4 = 36°
∠DOB = x + 9 = 16 + 9 = 25°
Example: If (2x + 17)° and (x + 4)° are complementary, what is the value of x?
(2x + 17) + (x + 4) = 90° (Given as complementary angles)
3x + 21 = 90
3x = 69 implies x = 23
- Find the value of ∠YOZ, if XOY is a straight line.
- If (5a + 42)° and (22 – a)° are supplementary angles, find a.
- Find the measure of ∠DOC.
- AB and CD intersect at O. If ∠AOD = 146°, find ∠BOD.
- Find x in the given figure.
Give Your Child The eTutorWorld Advantage
Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. eTutorWorld provides the best K-12 Online Tutoring Services so you can learn from the comfort and safety of your home at an affordable cost.
Be it an exam, class test or a quiz, eTutorWorld’s Math, Science and English tutors are responsible for your academic progress. Meet your personal coach at your convenient day and time to get help for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. All our tutors are graduates and bring with them years of teaching experience to the tutoring lessons.
Our ‘Learning by Design’ methodology makes sure that each student is at the center of the teaching-learning process. All tutoring sessions start with a question to the student ‘What do you want to learn today?’ Hence, tutors diagnose your skills and recognize your requirements before the actual tutoring happens. Post every tutoring session, an individualized worksheet is emailed to the student to assimilate learned concepts. Regular formative assessments are used to evaluate a student’s understanding of the subject.
The state of the art technology used is stable, user friendly and safe. All you need is a computer or a tablet and an internet connection. The easy-to-use web conferencing software requires a one time download, using which the student can talk and chat to the tutor, annotate on an interactive shared whiteboard or even share documents, assignments or worksheets.
All tutoring sessions are recorded and made available for a month so you can review concepts taught.
Email or call our support team with any issues or questions – we are here for you 24X7.
Also, download free printable math and science worksheets in pdf format and solve SCAT and SSAT Practice Tests online. Sign up for a Free Trial Lesson Today!
Thousands have taken the eTutorWorld Advantage – what are you waiting for?
© 2019 eTutorWorld - Online Tutoring and Test Prep | All rights reserved