In an isosceles triangle- one of the equal angles measures 50- - The sum of all the exterior angles of the same triangle is

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Standard VII

Mathematics

Exterior Angle

In an isoscel...

Question

In an isosceles triangle, one of the equal angles measures $50^{\circ}$ . The sum of all the exterior angles of the same triangle is ___ (in degrees).

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Solution

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 $(180 - x)^{\circ}$ , $(180 - y)^{\circ}$ , $(180 - z)^{\circ}$
Using angle sum property of a triangle,
(180 - x) + (180 - y) + (180 - z) = 180
540 - (x + y + z) = 180
$∴$ x + y + z = $360^{\circ}$

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In an isosceles triangle, one of the equal angles measures 50∘. The sum of all the exterior angles of the same triangle is ___ (in degrees)​.

In an isosceles triangle, one of the equal angles measures $50^{\circ}$ . The sum of all the exterior angles of the same triangle is ___ (in degrees).