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Question

# A triangle is constructed such that one of its side 10 cm, another side is of length 9 cm and the angle opposite to the side of length 9 cm is 60∘. This construction results in the formation of two triangles. Let us call the third vertex of the smaller triangle as C1 and the third vertex of the bigger triangle as C2, as shown in the image below. (image here) Then x∘ + y∘ equals

A

78

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B

82

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C

86

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D

89

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Solution

## The correct option is D 89∘ Step 1: Draw the base line AB of the length 10 cm. Step 2: Measure the angle A with your protractor. Make a mark at 60 degrees and draw a line from A passing through the mark. Now we must locate C. It should be 9 centimetres from B and also should be on the upper line, in order to form the required triangle. All points at a distance of 9 cms from B are on the circle centred at B of radius 9 cm. Thus we have the next step. Step 3: Draw a circle with centre at B and radius 9 cm. This circle cuts the line through A at two points. Name the third vertex of the smaller triangle as C1 and the third vertex of the bigger triangle as C2. (image here) Now, from the above construction we see that ∠ABC1 = 15∘ and ∠AC2B = 74∘. i.e., x = 74 and y = 15 Then, x∘ + y∘ = 74∘ + 15∘ = 89∘

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