Question
Answer: Option A
:
A
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. Fig1:
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∘
ΔPQRis an obtuse angled triangle as one of the angles measures 130°.
2. Fig 2:
ΔABCis 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 angledtriangle.
3. Fig3:
ΔXYZis an isosceles as well as an obtuse angled triangle as angleY measures 110°.
4. Fig4:
ΔMNOis an isosceles as well as a right angled triangle.
Hence, only Fig1and Fig3are isosceles as well as obtuse angledtriangles.
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:
A
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. Fig1:
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∘
ΔPQRis an obtuse angled triangle as one of the angles measures 130°.
2. Fig 2:
ΔABCis 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 angledtriangle.
3. Fig3:
ΔXYZis an isosceles as well as an obtuse angled triangle as angleY measures 110°.
4. Fig4:
ΔMNOis an isosceles as well as a right angled triangle.
Hence, only Fig1and Fig3are isosceles as well as obtuse angledtriangles.
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