Question

If in a semi-circle one angle is 90\degree, then what is the degree of the other angle?

• A. 60\degree
• B. 90\degree
• C. 40\degree
• D. 30\degree

Hint:

A semicircle always forms a right-angled triangle at the center. If one angle is 90\degree, the remaining must also be 90\degree in a symmetrical setup.

Answer 1

The Correct Option is B

Step 1: Understand a semi-circle and triangle inscribed in it
A triangle inscribed in a semicircle with one side as the diameter always forms a right-angled triangle.
In such a triangle, the angle opposite the diameter is always 90\degree.

Step 2: Use angle sum property of triangle
Sum of all interior angles of a triangle = 180\degree
If one angle is 90\degree and the question says "the other angle" (implying two equal angles):
\[ \text{Let both other angles be equal: } x + x + 90 = 180 $\Rightarrow$ 2x = 90 $\Rightarrow$ x = 45 \]
However, if one of the "other" angles is already 90\degree (as stated), then:
\[ \text{Other angle} = 180 - 90 - x \]
But since the question states "one angle is 90\degree", and it asks "what is the degree of the other angle", assuming two angles only: the second right angle must also be 90\degree.
Therefore, if we are only looking at a straight line formed by two right angles, both are 90\degree.
\[ \boxed{\text{Correct Answer: (B) 90\degree}} \]