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The exterior angle of a triangle is equa...

The exterior angle of a triangle is equal to the sum of two

A

Exterior angles

B

Interior opposite angles

C

Alternate angles

D

Interior angles

Text Solution

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The correct Answer is:
B
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Take three different colour sheets , place one over the other and draw a triangle on the top sheet. Cut the sheets to get triangles of different colour which are identical. Mark the vertices and the angles as shown. Place the interior angles angle1,angle2 and angle3 on a straight line, adjacent to each other, without leaving any gap. What can you say about the total measure of the three angles angle1,angle2 and angle3 ? Can you use the same figure to explain the ''Exterior angle property'' of a triangle ? If a side of a triangle is stretched, the exterior angle so formed is equal to the sum of the two remote interior angles.

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Knowledge Check

  • The exterior angle of a triangle is 120^(@) and one of its interior opposite angle 58^(@) , then the other opposite interior angle is________.

    A
    `62^(@)`
    B
    `72^(@)`
    C
    `78^(@)`
    D
    `68^(@)`

  • An exterior angle of a triangle is 70^@ and two interior opposite angles are equal. Then measure of each of these angle will be

    A
    `110^@`
    B
    `120^@`
    C
    `35^@`
    D
    `60^@`

  • If an exterior angle of a triangle is 115^@ and one of the interior opposite angles is 35^@ , then the other two angles of the triangle are

    A
    `45^@, 60^@`
    B
    `65^@, 80^@`
    C
    `65^@, 70^@`
    D
    `115^@, 60^@`

    • Similar Questions

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    If the exterior angle of a triangle is 140^@ and its interior opposite angles are equal, find all the interior angles of the triangle.

    Equilateral triangles are drawn on the three sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides.

    If the square of the longest side of a triangle is equal to sums of squares of other two sides, then the triangles is …………..

    Prove by vector method, that in a right angled triangle the square of h the hypotenuse is equal to the sum of the square of the other two sides.

    Prove that in a right triangle, the square of the hypotenure is equal to the sum of the squares of the others two sides.

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