Question Video: Identifying the Relation between Sides and Corresponding Angles in a Triangle Using Supplementary Angles Mathematics

Which of the following is true? [A] ๐ด๐ต = ๐ด๐ถ [B] ๐ถ๐ด = ๐ถ๐ต [C] ๐ต๐ถ = ๐ต๐ด


Video Transcript

Which of the following is true? Option (A) ๐ด๐ต equals ๐ด๐ถ, option (B) ๐ถ๐ด equals ๐ถ๐ต, option (C) ๐ต๐ถ equals ๐ต๐ด.

In the diagram, we have a triangle ๐ด๐ต๐ถ, weโ€™ve got a line ๐ต๐ถ, and weโ€™ve got this ray ๐ต๐ด. In the options that weโ€™re given, weโ€™re really looking to see if thereโ€™s a pair of lines which are equal in length. Weโ€™re not given any hash marks on any of the lines, which would indicate that two are equal. So letโ€™s have a look at the angles instead.

If we use the fact that the angles on a straight line add up to 180 degrees, then we should be able to work out this angle ๐ด๐ถ๐ต and this angle ๐ด๐ต๐ถ. Starting with angle ๐ด๐ถ๐ต, we can write that thatโ€™s equal to 180 degrees subtract 98 degrees. We can work this out by calculating 180 degrees subtract 100 degrees and then adding on two, which would give us a value of 82 degrees. We can add this value to the diagram. The next angle, angle ๐ด๐ต๐ถ, must be equal to 180 degrees subtract 131 degrees. Subtracting 130 degrees and then another one degree would give us 49 degrees.

Now that weโ€™ve found these two angles in this diagram, we might think that itโ€™s not very helpful. But letโ€™s see if we can have a look at calculating the other angle in the triangle ๐ด๐ต๐ถ. We should remember that the angles in a triangle add up to 180 degrees. So weโ€™ll have our unknown angle ๐ถ๐ด๐ต plus angle ๐ด๐ถ๐ต, which we worked out as 82 degrees, plus the angle ๐ด๐ต๐ถ, which we worked out as 49 degrees, all must add to give 180 degrees. This means angle ๐ถ๐ด๐ต plus 131 degrees equals 180 degrees. Subtracting 131 degrees from both sides of this equation gives us that angle ๐ถ๐ด๐ต is equal to 49 degrees. We can then add that onto our diagram and see if thereโ€™s anything to notice.

Well, we should hopefully see that we have in fact got two angles that are the same size. Both of these are 49 degrees. This means that weโ€™ve got an isosceles triangle here in triangle ๐ด๐ต๐ถ. Any triangle that has two equal angles must have two equal sides. And therefore, itโ€™s an isosceles triangle. The two sides that are equal will be this side ๐ถ๐ด and this side ๐ถ๐ต. We can then give our answer that ๐ถ๐ด equals ๐ถ๐ต, which was the option given in option (B).

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