An exterior angle of a triangle is 15°& one of the interior opposite angle is 35° find the other two angles of a triangles

Exterior angle of a triangle of the sum of two opposite interior angles.

So I see a typo in your question
The way to do this is

Exterior angle= two opposite interior angle s
Or exterior = x+ another interior
Find x
And then
X+ another interior+ y= 180
Solve for y coz you already found x
(Sum of 3 angles of a triangle= 180°)

To find the other two angles of the triangle, we can use the fact that the sum of the interior angles of a triangle is always 180 degrees.

Let's denote the three interior angles of the triangle as A, B, and C.

We are given that one of the interior opposite angles (angle A) is 35 degrees, and the exterior angle (angle D) is 15 degrees.

The exterior angle is equal to the sum of the two non-adjacent interior angles. So, angle D = angle B + angle C.

Since angle D is given as 15 degrees, we have:

15 = angle B + angle C

Now, we know that the sum of the three interior angles is 180 degrees. So we can write:

angle A + angle B + angle C = 180

Substituting the given values, we have:

35 + angle B + angle C = 180

Now, let's rearrange the equation to solve for angle B:

angle B = 180 - 35 - angle C

Substituting this value into the first equation, we have:

15 = (180 - 35 - angle C) + angle C

Simplifying the equation further:

15 = 180 - 35

15 = 145 - angle C

Now, subtracting 145 from both sides of the equation:

15 - 145 = - angle C

-130 = - angle C

Multiplying by -1 to both sides of the equation:

130 = angle C

So, angle C is 130 degrees.

Now, substituting this value into the equation for angle B:

angle B = 180 - 35 - angle C

angle B = 180 - 35 - 130

angle B = 180 - 35 - 130

angle B = 15 degrees

Therefore, the other two angles of the triangle are 15 degrees and 130 degrees.