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.
![finding angle measures](https://www.etutorworld.com/wp-content/uploads/2018/10/findingangle-300x110-300x110.jpg)
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°.
![finding angle measures](jpg/findingangle1-1.jpg)
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.
![finding angle measures](https://www.etutorworld.com/wp-content/uploads/2018/08/findingangle2-300x166.jpg)
![finding angle measures](https://www.etutorworld.com/wp-content/uploads/2018/10/findingangle3-300x248-300x248.jpg)
∠ AOB and ∠ BOC are adjacent angles with OB as the common arm.
![finding angle measures](https://www.etutorworld.com/wp-content/uploads/2018/12/findingangle4.jpg)
![finding angle measures](https://www.etutorworld.com/wp-content/uploads/2018/12/findingangle5.jpg)
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°
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