Finding Angle Measures
Grade 8 Math Worksheets
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°.
Right Angle
One fourth the rotation will have a measure of 90°, which is called a ‘right angle’.
Acute Angle
An angle with a measure less than 90° is called an ‘acute’ angle.
Obtuse Angle
An angle with its measure lying between 90° and 180° is called an ‘obtuse’ angle.
Reflex Angle
An angle with its measure lying between 180° and 360° is called a ‘reflex’ angle.
Adjacent Angles
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
Check Point
- 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.
Answer key
- 118°
- 29
- 110°
- 34°
- 45°
Personalized Online Tutoring
eTutorWorld offers affordable one-on-one live tutoring over the web for Grades 2-12, Test Prep help for Standardized tests like SCAT, CogAT, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.
For answers/solutions to any question or to learn concepts, take a FREE Demo Session.
No credit card required, no obligation to purchase.
Just schedule a FREE Sessions to meet a tutor and get help on any topic you want!
Learn more about Scientific Method and other important topics with 7th Grade Science Tutoring at eTutorWorld. Our expert science tutors break down the topics through interactive one-to-one sessions. We also offer the advantage of customized lesson plans, flexible schedules and convenience of learning from home.
Pricing for Online Tutoring
Tutoring Package | Validity | Grade (1-12), College |
---|---|---|
5 sessions | 1 Month | $124 |
1 session | 1 Month | $25 |
10 sessions | 3 months | $239 |
15 sessions | 3 months | $354 |
20 sessions | 4 months | $449 |
50 sessions | 6 months | $1049 |
100 sessions | 12 months | $2049 |