Angles at a Point
Primary 5 angles at a point questions: the angles round one point fill 360°, so find the missing one, even a reflex angle the long way round.
Questions in this lesson
Transcript
A B C D is a square and B C E is a triangle. E B is the same length as E C and angle B E C is 44 degrees. Find angle x. Try it first. Pause if you like. Look at the point C. x is the angle marked there, and its curve is drawn on the outside of the figure. It goes more than half way round the point, so x is bigger than one hundred and eighty degrees. Three angles meet at C: angle B C D in the square, angle B C E in the triangle, and x on the outside. Angles at a point: the three of them add up to three hundred and sixty degrees. Angle B C D is the square's corner, so it is 90 degrees. In the triangle, E B and E C are the same length, so the two angles at B and at C are equal. The three angles in a triangle add up to one hundred and eighty degrees, so angle B C E is one hundred and eighty minus 44, divided by 2, which is 68 degrees. Now x is the rest of the full turn. Three hundred and sixty minus 90 minus 68 is two hundred and two degrees.
Your turn. O A, O B and O C meet at the point O. Angle A O B is two hundred and fourteen degrees and angle B O C is 63 degrees. Find angle y. Try it first. Pause if you like. Two hundred and fourteen degrees is bigger than one hundred and eighty, so that angle goes the long way round O. The three angles at O make one full turn, so y is three hundred and sixty minus two hundred and fourteen minus 63, which is 83 degrees. All the way round O is one full turn, three hundred and sixty degrees. Two hundred and fourteen and 63 are two of the three angles. 83 degrees is what is left. Angles at a point add up to three hundred and sixty degrees, even when one goes the long way round.