How many degrees is angle x?
A normal-level "Angle" problem.When a triangle appears inside a circle, hunt for "all radii are equal" first. An isosceles triangle falls out, and the angles follow one after another.
GivenO is the centre of the circle; A and B are on the circle, and angle AOB = 70°
Hints
- OA and OB both run from the centre to the edge — they are radii. A few more radii are drawn dotted: every radius of a circle is the same length.
- So triangle OAB has two equal sides: it is isosceles. Whenever a triangle turns up in a circle problem, look for this first.
- Being isosceles, its two base angles are equal too: the x we want and the angle opposite it are the same size.
- A triangle's angles total 180°. Take off the 70° at the top and 110° is left — that is two x's.
- Two x's make 110°, so the answer is 110 ÷ 2.
Answer 55°
More "Angle" problems
- How big is angle x?
- How many degrees is angle x?
- What is A＋B＋C＋D＋E?
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- How many degrees is angle x?