Question

12. In the given figure, find the measure of the remaining angles of the given triangle.
56
101​

Answer 1

Solution :

Here in the figure , we have to find the measures of the remaining angles. .

For the given triangle

One angle is 56° and the other is x° .

The exterior opposite angle is 101°

According to the exterior angle theorem , the exterior angle of any triangle is equal to the sum of its opposite interior angles.

So , we can say that

56° + x = 101°

> x = 101° - 56°

> x = 45° .

Also

For a triangle , sum of all it's interior angles is 180°

Therefore the third angle is -

> 180° - 56° - 45°

> 180° - 101°

> 79°.

Answer - The measures of all the angles of the given triangle are 56°, 45° and 79° respectively .

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Answer 2

SO ACCORDING TO THE PIC ATTACHED BELOW

ANGLE ABD + ANGLE ABC  = 180

ANGLE ABC = 180-101

=79

ANGLE ABC + ANGLE BCA + ANGLE BAC =180 (ANGLE SUM PROPERTY)

79+56+ANGLE X =180

X= 180-79+56

X= 180-135

X= 45 DEGREES