Angles Between Parallel Lines
Primary 5 angles between parallel sides questions: carry 180° across a trapezium or parallelogram, then finish in the triangle a diagonal makes.
Questions in this lesson
Transcript
A B C D is a trapezium with A B parallel to D C, and D E C is a triangle inside it. The figure is not drawn to scale. Angle A B C is one hundred and sixteen degrees, angle B C E is 40 degrees and angle E D C is 30 degrees. Find angle D E C. Try it first. Pause if you like. The angle we want sits inside the triangle. One of that triangle's other angles is given: angle E D C is 30 degrees. Angle E C D is not given. The only other angle we have is angle A B C, right across the figure at the corner B. The arrowheads say line A B and D C are parallel. The side B C runs from one of them to the other. The two angles between the parallel sides, angle A B C and angle B C D, add up to one hundred and eighty degrees. So angle B C D is one hundred and eighty minus one hundred and sixteen, which is 64 degrees. The bracket underneath says which property gave it. The line C E cuts angle B C D into two parts. One of them is given: angle B C E is 40 degrees. So angle E C D is 64 minus 40, which is 24 degrees. Now the triangle has two of its three angles: 24 degrees and 30 degrees. The three angles in a triangle add up to one hundred and eighty degrees. So angle D E C is one hundred and eighty minus 24 minus 30, which is one hundred and twenty six degrees.
Your turn. P Q R S is a trapezium with P Q parallel to S R. Angle P Q R is one hundred and eighteen degrees and angle Q S R is 43 degrees. Find angle x. Try it first. Pause if you like. P Q and S R are the parallel sides, and Q R runs from one to the other. So angle Q R S is one hundred and eighty minus one hundred and eighteen, which is 62 degrees. Now triangle Q R S has two of its angles: 62 degrees and 43 degrees. So angle x is one hundred and eighty minus 62 minus 43, which is seventy five degrees. P Q and S R are the parallel sides. One hundred and eighteen degrees and 62 degrees are the two angles between them. Together they are one hundred and eighty degrees. The parallel sides give the missing angle, and the angle sum of a triangle gives the rest.