Question

Please help!!
What is the value of a + b?
A. 110
B. 135
C. 125
D. 145

Answer 1

The inscribed angle a will be half of that central 90 degree angle, so a=45 degrees.

Answer 2

not an option

Answer 3

option what ?

Answer 4

ouh,hahaha...hold on..hehe

Answer 5

First notice that the central angle 90 degrees is twice the inscribed angle 'a'. Hence:\[\bf 2\angle a = 90 \implies \angle a=45\] Now to find 'b', observe the following diagram:Notice that by drawing line CB, we notice that the central angle is 110 degrees. We also notice one more important thing, the line BC is the radius of the circle connecting the centre with the circumference. And the line with the arrow is tangent to the circle exactly where the line BC touches. Through the tangent-angle theorem, we know that the angle that BC forms with the tangent line is 90 degrees. Now notice the following:\[\bf \angle b=90-\angle CBA\]To find what angle CBA is, we notice that the central angles 90 and 110 sum up to 200 degrees. This implies that the central angle ACB subtended by the arc AB must be 160 degrees. We also know that triangle ABC is isosceles since two of its sides are the radii of the circle. Since angle ACB is 160, and the triangle is isosceles, then the other two angles must be the same and all the angles add up to 180 degrees, then each of the remaining angles CBA and CAB is:\[\bf \frac{180-\angle ACB}{2}=\frac{180-160}{2}=10=\angle CBA =\angle CAB\]Now plugging this value back in to the angle b equation we get b as:\[\bf \angle b =90-\angle CBA = 90-10=80\]We already evaluated angle so now we add the two andgles and we get:\[\bf \therefore \ \angle a + \angle b = 80°+45°=125°\]

Answer 6

@ehmuleeee

Answer 7

nice bro..