Question

# Which of the following triangles are isosceles as well as obtuse-angled triangles?

A

Fig 1 and Fig 3 only

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B

Fig 2 and Fig 3 only

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C

Fig 1, Fig 2 and Fig 4 only

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D

Fig 1, Fig 2 and Fig 3 only

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Solution

## The correct option is A Fig 1 and Fig 3 only An obtuse angled triangle is the triangle in which one of the angles is greater than 90∘. An isosceles triangle is the triangle in which two sides are equal. 1. Fig 1: ΔPQR is isosceles [∵PQ=PR] ⇒∠Q=∠R [∵ angles opposite to equal sides of a triangle are equal] ∠P+∠Q+∠R =180∘ [angle sum property of a triangle] ∠P+25∘ +25∘ =180∘ ⇒∠P=180∘ −50∘=130∘ ΔPQR is an obtuse angled triangle as one of the angles measures 130°. 2. Fig 2: ΔABC is isosceles [∵AB=AC] Similarly as above, we can find the angles of this triangle. ∠A=35∘,∠B=∠C=72.5∘ Since all angles are less than 90∘, ΔABC is an acute angled triangle. 3. Fig 3: ΔXYZ is an isosceles as well as an obtuse angled triangle as angle Y measures 110°. 4. Fig 4: ΔMNO is an isosceles as well as a right angled triangle. Hence, only Fig 1 and Fig 3 are isosceles as well as obtuse angled triangles.

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