UPSC CDS I 2025 Mathematics Paper

Given:
Triangle ABC
Bisectors of angles A and C intersect and form an angle =130∘
Find angle B
Formula used:
Angle between bisectors of A and C inside triangle =90∘+B∕2
Calculations:
Given, angle between bisectors =130∘
Using formula: 90+B∕2=130
‌⇒B∕2=130−90
‌⇒B∕2=40
‌⇒B=80∘