Two exterior angles of a triangle equal 100° and 150°. find all the interior angles.

The interior angles for this triangle are 80º, 30º and 70º.

Step-by-step explanation:

The sum of a interior angle with it's respective exterior angle is also always 180º.

So, for the exterior angle that is 100º, we can find the first interior angle of the triangle

100º + A1 = 180º

A1 = 180º - 100º

A1 = 80º

The first interior angle of this triangle is A1 = 80º;

For the exterior angle that is 150º, we can find the second interior angle of the triangle.

150º + A2 = 180º

A2 = 180º - 150º

A2 = 30º

The second interior angle of this triangle is A2 = 30º.

From here, to find the third interior angle, we apply the following definition

The sum of the three interior angles of a triangle is always 180º.

So:

A1 + A2 + A3 = 180º

80º + 30º + A3 = 180º

110º + A3 = 180º

A3 = 180º - 110º

A3 = 70º

The third interior angle of this triangle is A3 = 70º.

The interior angles for this triangle are 80º, 30º and 70º.

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step-by-step explanation:

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