A triangle has one of the inner angles of 30 degrees and one of the outer angles of 40 degrees. find the rest of the interior corners.
From the condition we know that a triangle has one of the inner angles equal to 30 °, and one of the outer angles is 40 °.
In order to find all the angles of a triangle, we must remember what is the sum of adjacent angles and the theorem on the sum of the angles of a triangle.
So, the sum of adjacent angles is 180 °. Now we can find the degree measure of the inner corner of the triangle adjacent to the outer one:
180 ° – 40 ° = 140 °.
We now know the two corners of the triangle. By the theorem on the sum of the angles of a triangle, the sum of the angles of a triangle is 180 °.
180 ° – (140 ° + 30 °) = 180 ° – 170 ° = 10 °.
Answer: 140 °; 10 °.
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