6.6.3 Angles and Tangents of Circles, PT3 Practice


Question 7:
Diagram below shows a circle with centre O.

Find the value of x.

Solution:
Q R O = 38 o , O R S = 44 o Q R S = 38 o + 44 o = 82 o x o = 82 o × 2 x o = 164 o x = 164



Question 8:
Diagram below shows a circle. QTS is the diameter of the circle and PTR is a straight line.
Find the value of x.

Solution:
R P S = 90 o 42 o = 48 o x o = 48 o + 37 o = 85 o



Question 9:
Diagram below shows a circle with centre O. PQR is a straight line.

Find the value of x and of y.

Solution:
In cyclic quadrilateral,
Angle at Q = 180o – 70o = 110o
x2 = exterior angle at Q
= 180o – 110o
= 70o
x = 70

yo = reflex angle at O
yo = 360o – (70o × 2)
yo = 220o
y = 220


Question 10:
In diagram below, ABCD and DEFG are straight lines.
Find the value of x and of y.

Solution:
x=95 ( exterior of B cyclic quadrilateral ) CBF+BFE+ 95 o + 110 o = 360 o  CBF+BFE+ 205 o = 360 o CBF+BFE= 155 o y o +CBF+BFE= 180 o    y o + 155 o = 180 o   y=25

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