How many degrees is angle x?
A hard-level "Angle" problem.The dented vertex equals the sum of the other three angles. One construction line splits it into two triangles, so you can rebuild the rule on the spot instead of memorising it.
Hints
- Vertex P is pushed inwards. In this shape neither the triangle rule nor the quadrilateral rule applies.
- So draw just one construction line: join A to P and carry it on outwards to a point D. The dent disappears and two triangles come into view.
- Look at triangle ABP on the left. An exterior angle equals the sum of the two non-adjacent interior angles, so ∠BPD = ア + 25°.
- The same argument on the right, in triangle ACP: ∠CPD = イ + 30°.
- x is ∠BPD plus ∠CPD, i.e. x = (ア + イ) + 25 + 30. And ア + イ is just the two halves of angle A that AP cut apart — so it is angle A itself, 50°.
- So x = angle A + angle B + angle C. 50 + 25 + 30 is the answer.
Answer 105°
More "Angle" problems
- How big is angle x?
- How many degrees is angle x?
- What is A＋B＋C＋D＋E?
- How big is angle BIC?
- How many degrees is angle x?
- What is the angle at the centre of the sector?