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If one angle of a triangle is equal to t...

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

A

an isosceles triangle

B

an obtuse triangle

C

an equilateral triangle

D

a right triangle

Text Solution

Verified by Experts

The correct Answer is:
D
Let the angles of a `DeltaABC be /_A, /_B and /_C`.
Given, `" " /_A = /_B + /_C" "` …(i)
In `DeltaABC , " " /_A + /_B +/_C = 180^(@)" " ["sum of all angles of a triangle is "180^(@)`] ….(ii)
From Eqs. (i) and (ii) ,
`/_ A + /_A 180^(@)`
`implies " " 2/_A = 180^(@)`
`implies " " /_A = 180^(@) /2`
`:. " " /_A = 90^(@)`
"Hence, the triangle is a right triangle".
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Knowledge Check

  • If one angle of a triangle is equal to half the sum of the other two equal angles, then the triangle is :

    A
    isosceles
    B
    scalene
    C
    equilateral
    D
    right angled

  • If each angle of a triangle is less than the sum of the other two, then the triangle is

    A
    obtuse angled
    B
    right angled
    C
    acute angled
    D
    equilateral

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