## Lakshya Education MCQs

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

Options:
 A. Fig 1 and Fig 3 only B. Fig 2 and Fig 3 only C. Fig 1, Fig 2 and Fig 4 only D. Fig 1, Fig 2 and Fig 3 only
: 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=18050=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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## More Questions on This Topic :

Question 1. Consider the figure:

If A = 50​, B = 70​ and x = 2y, then x+y is equal to (in degrees)

__

: By Exterior angle property of triangles,
x + y = A + B
=50+ 70
=120
Question 2. The third side of a triangle must be greater than the difference between the other two sides.
1.    True
2.    False
: A

The third side of a triangle must be greater than the difference between the other two sides.
Question 3. A triangle with all the three angles less than 60 degree is possible.
1.    True
2.    False
: B

A triangle with all the three angles less than 60 is not possible, as thesum of all the angles of a triangle is 180​.
Question 4. The sum of all the exterior angles of a triangle is ___  (in degrees)​.

: Let the exterior angles of the triangle be x, y and z respectively.

Then by exterior angle property,interior angles of the triangle will be (180x)​, (180y)​​, (180z)​​
Using angle sum property of a triangle, (180- x) + (180- y) + (180- z) = 180 540-(x + y + z) =180 Therefore, x + y + z = 360
Question 5. A __ connects a vertex of a triangle to the mid-point of the opposite side.

: A median is line joining a vertex of a triangle to the mid-point of the opposite side.
Question 6. The square of the hypotenuse is equal to the sum of the squares of the other two sides. This relation holds for all types of triangles.
1.    True
2.    False