1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# A triangle is constructed such that one of its side 8 cm, another side is of length 5.5 cm and the angle opposite to the side of length 5.5 cm is 40∘. 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. Then x∘ + y∘ equals

A

160

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

180

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C

140

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

120

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is B 180∘ Step 1: Draw the base line AB of the length 8 cm. Step 2: Measure the angle A with your protractor. Make a mark at 40 degrees and draw a line from A passing through the mark. Now, we must locate C. It should be 5.5 cm from B and also should be on the upper line, in order to form the required triangle. All points at a distance of 5.5 cm from B are on the circle centred at B of radius 5.5 cm. Thus, we have the next step. Step 3: Draw a circle with centre at B and radius 5.5 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. Now, from the above construction, using protractor, we see that ∠AC1B = 110∘ and ∠AC2B = 70∘. i.e., x = 110 and y = 70 Then, x∘ + y∘ = 110∘ + 70∘ = 180∘

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Let's Build Triangles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program