How big is angle BIC?
A hard-level "Angle" problem.You never learn B and C separately — but knowing their sum is enough to know the sum of their halves. This is practice at using unknowns without solving for them.
GivenIn triangle ABC, angle A is 50°. The bisectors of angles B and C meet at I.
Hints
- We cannot know angles B and C separately. But the three angles add to 180°, so together they are 130°. That much we do know.
- BI and CI cut angles B and C exactly in half. So the angles we need in triangle IBC are half of B and half of C.
- This is the key step. Half of one plus half of the other is half of the total. B and C add to 130°, so their halves add to 130 ÷ 2 = 65° — without ever knowing B and C separately.
- Now just use the angle sum of triangle IBC: 180 − 65 = 115°.
- Tidied up, the answer is 90 + angle A ÷ 2. Whatever A is, angle BIC is always more than 90°.
Answer 115度
More "Angle" problems
- How big is angle x?
- How many degrees is angle x?
- What is A＋B＋C＋D＋E?
- How many degrees is angle x?
- How many degrees is angle x?
- What is the angle at the centre of the sector?