If PQ is straight line, then ___________ (_____________)
If AB & BC are straight lines, then ______ & ______(_________)
If AB and CD are parallel lines. a) ∠s = ∠r (_________________) b) ∠q = ∠s (_________________) c) ∠p + ∠q = 180° (_________________)
(i) (ii) (iii)
Angle BAX, Angle CBX, Angle BDX.
How to Read Bearings
To read the bearing of B from A: 1. Draw the North line from A. 2. Join A to B. 3. From A, measure the clockwise angle. 4. Bearing is always written in 3 digit.
Useful properties - Sum of interior angles
Find the bearing of (a)#A from O, (b)#B from A, (c) A from B.
Useful properties - Alternate angles
Find the bearing of (d) O from B.
Q1. The points P, Q and R form an equilateral triangle and the bearing of Q from P is. Find (a) the bearing of R from P, (b) the bearing of R from Q, (c) the bearing of P from R.
Solve Q2. In the diagram, R is due east of P and angle PQR = 800. If the bearing of Q from R is 2000, find (a) angle QRP, (b) the bearing of Q from P.
Angles of Polygon
∠p + ∠q + ∠r = _____ (∠ sum of a ∆)
∠a + ∠b + ∠c + ∠d = _____
Sum of int. angles = (n – 2) × 180o
If the polygon is regular, Size of an angle = _________
Int. Â angle
Ext. Â angle
Int. angle + Ext. angle = ________
Sum of exterior angles = ___________________
1. Sum of interior angles = ___________________
2. Sum of exterior angles = ___________________
3. 1 Interior + 1 Exterior = ___________________
Solve Q1. Find the unknown value.
Solve Q2. Find the unknown value.
Q3. Given that a regular n-sided polygon has an interior angle twice the exterior angle, find the number of sides that the polygon has.
Q4. The size of each interior angle of a regular polygonis 11 times the size of each exterior angle. (a) Find the size of each exterior angle. (b) How many sides does the polygon have?
Q5. An exterior angle of an octagon is 66째 while the other seven exterior angles are each equal to x째. a) Calculate the value of x. b) Find the smallest interior angle of the octagon.
Solve Q6. AB, BC and CD are three adjacent sides of a regular 12-sided polygon. Calculate the values of (a) ∠ ABC, (b) ∠ACD.
Q7. The diagram shows part of a regular polygon with n sides. Each exterior angle of this polygon is 12Â°. Find (a) the value of n, (b) âˆ ACD.
C D E
Angles on Circles
OR: ___________ PQ: ___________
∠FXM = 90° (_________________________)
AC: _____________ ABC: ______________ Shaded part: _____________
∠FYM = ∠FXM (_________________________________)
∠ADC + ∠ABC = 180° ∠BAD + ∠BCD = 180° (______________________________)
∠FOM = 2 × ∠FXM (__________________________________)
∠OTX = 90° (______________________)
Q1. What is the value of x? State the reason.
Q2. What is the value of x? State the reason.
Q3. What is the value of x? State the reason.
Q4. What is the value of x? State the reason.
Q5. What is the value of x? State the reason.
Q6. What is the value of x? State the reason.
Q7. What is the value of x? State the reason.
Q8. What is the value of x? State the reason.
Q9. What is the value of x? State the reason.
Q10. What is the value of x? State the reason.
Q11. What is the value of x? State the reason.
Q12. What is the value of x? State the reason.
Q13. What is the value of x? State the reason.
Solve Q14. Find ∠ OKN
Find ∠ BAC
Solve Q15. Find âˆ ACB
Q16. Find ∠ APD
Solve # Q17. In the figure, QS is a diameter and T is the intersection of QS and PR. # If ∠ RSQ = 72° and ∠ SQP = 28°, find # (a)#∠ SPR,# (b) ∠ PTS.
Solve Q18. O is the centre of a circle. PCQ is tangent to the circle at C. ∠ ABC = 98° and ∠ BCP = 55°. Stating your reasons clearly, find (a) reflex ∠ AOC ,# (b)# ∠ BAO.
Solve Q19. AC is the diameter of the circle. XAB and XDC are straight lines and DE =EC. Given that ∠ BXC = 20º and ∠ ACB = 50º, find, giving your reasons in the working space, (a) ∠ BDC, (b) ∠ XCA, (c) ∠ DEC.
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