Question

ABC is a triangle such that BC is the diameter of the circle and the point A lies on the circle.Then the half of the angle measure of A is

Answer 1

Answer:

if BC is passing through diameter

then the opposite angle

i.e angle A should be90° half of it will be45°

Answer 2

Half of the measure of angle A will be 45°.

Given,

ABC is a triangle such that BC is the diameter of a circle,

point A lies on the circle.

To find,

Half of the measure of angle A.

Solution,

ABC is given to be a triangle, such that BC is the diameter of a circle.

Now, we know that if an angle is in the semicircle, then its measure is always 90°.

Or, the angle subtended by the diameter on any point on the circle is 90°.

Since point A lies on the circle, it can be seen that ΔABC will be a right-triangle right angled at A, and,

∠A or ∠BAC will be 90°.

⇒ m ∠A = 90°.

Thus, half of the measure of ∠A will be

$\frac{1}{2} m \angle A=\frac{90}{2}$

$\frac{1}{2} m \angle A= 45 \textdegree$.

Therefore, half of the measure of angle A will be 45°.