The names of angles are in three categories:

• by size
• as a sum of a pair of angles
• according to their specific position

b) as a sum of a pair of angles

c) according to their specific position

Names of angles by relating two positions

Vertically opposite angles, see image below:

From the figure below a and c, b and d are vertically opposite angles.

Other angles in this class include:

• corresponding angles,
• alternate angles
• co-interior (adjacent) angles,

(See angle properties of parallel lines and transversals).

 

KCPE Topical Questions

Class 6

Angle properties

1. In the figure below, AB is parallel to ED. Angle ABE = 20⁰, angle EDB = 120⁰ and angle ECD = 70⁰. 

What is the size of the angle AEB?

A. 70⁰        B. 50⁰       C. 130⁰       D. 110⁰

 

2. In the figure below AE // BD, CD is perpendicular to AC, angle CDB = 24⁰ and angle BEA = 56⁰.

What is the size of the angle ABE?

A. 56⁰         B. 58⁰       C. 62⁰        D. 66⁰

 

3. In the figure below, CDEF is a straight line. CF is parallel to BA and BD is parallel to AE. Angle CBD = 44⁰ and BC = BD.

What is the size of angle AEF?

A. 44⁰       B. 136⁰      C. 68⁰      D. 112⁰

 

4. In the figure below, ABE is a straight line. DC is parallel to AE. Angle CBE = 110⁰ , angle ACB = 80⁰ and angle ADC = 100⁰.

What is the size of the angle CAD?

A. 30⁰         B. 50⁰      C. 40⁰       D. 80⁰

 

5. In the figure below, CDB is a straight line. Line CD = AD = DB. Angle ACB = 40⁰ 

What is the size of the angle ABD?

A. 80⁰       B. 40⁰        C. 50⁰         D. 100⁰

 

6. In the figure below, AE is parallel to BC. Line AB = AC = AD. Angle BAC = 52⁰ and ADE is a straight line.

What is the size of the angle CDE?

A. 116⁰        B. 58⁰         C. 128⁰         D. 122⁰

 

7. In the figure below, QS bisects angle PQR. Angle QPR = 56⁰, angle SRN = 84⁰ and PQ = PR. QRN is a straight line.

What is the size of the angle QSR?

A. 31⁰         B. 34⁰        C. 42⁰          D. 53⁰

 

8. In the figure below, ABCD is a quadrilateral in which angle DAB = 90⁰ and angle ABD = 36⁰. Line DA is parallel to CB and DB = DC.

What is the size of the angle BDC?

A. 36⁰       B. 54⁰      C. 72⁰      D. 60⁰  

 

9. In the figure below, MYRZ, XQZ, and RQS are straight lines. YX is parallel to RS. Angle MYX = 140⁰ and XQS = 60⁰

What is the size of the angle RZQ?

A. 80⁰       B. 120⁰      C. 40⁰          D. 60⁰

 

10. In the figure below, EFGH is a quadrilateral and EFH is an equilateral triangle. Angle EFG = angle EHG = 90⁰

What is the size of the angle FGH?

A. 60⁰            B. 90⁰             C. 120⁰             D. 30⁰

 

11. In the figure below, PQRS is a quadrilateral in which line PQ = line PR = line PS. Angle RPS = 68⁰. TQR is a straight line and line PQ is parallel to line SR.

What is the size of the angle TQP?

A. 62⁰        B. 68⁰      C. 118⁰        D. 124⁰

 

12. In the figure below, PQ is parallel to RS.

What one of the following statements is true?

A. x⁰ + t⁰ + z⁰ = 180⁰
B. y⁰ + t⁰ + z⁰ = 180⁰
C. x⁰ + y⁰ +z⁰ = 180⁰
D. x⁰ +y⁰ +t⁰ = 180⁰

 

13. In the figure below, line ADE is parallel to line BC. Angle DAB = 90⁰ and angle EDC = 110⁰. Line AD = DC.

What is the size of the angle ACB?

A. 25⁰           B. 35⁰        C. 45⁰         D. 55⁰

 

14. In the figure below, XY and XZ are straight lines meeting at X. Lines MN and PQ are parallel. Line XY intersects line MN and PQ at T and F respectively. Line XZ intersects lines MN and PQ at V and G respectively. Line XT = TV and angle PFY = 40⁰.

What is the size of angle TVZ?

A. 110⁰          B. 70⁰        C. 40⁰         D. 140⁰