What is the value of a + b+c? you may assume that the ray is tangent to the circle?
a. 86
b.150
c.133
d.47

Option c

Step-by-step explanation:

Given is a picture of a circle with two arcs angled 54 and 86.

a,b,c are the angles shown as the angle between a chord and tangent, angle between diameter and a chord and also angle between another chord and diameter

Recall the subtended angle theorem for circles

Angle subtended at the centre is double angle subtended at the circumference

Since arc below subtends 86 with centre it will subtend 43 degrees at the circumference.

ie. c= 43 degrees...i

Next is sum of a+b.

Recall tangent theorem that any tangent is perpendicular to the radius at the contact point.  Here a+b is the angle between tangent and radius

Hence a+b=90

Together

a+b+c = 133 degrees

Option c

b. x- 48 =120

step-by-step explanation:

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step-by-step explanation: