Find the degree measures of the angles if they are proportional to the numbers 5: 6: 7.
| September 5, 2021 | education
Since the degree angles of the triangle are proportional to the numbers 5/6/7, there is such a coefficient K, at which the ratio of the angles is 5 * K / 6 * K / 7 * K.
The sum of the interior angles of a triangle is 180, then:
5 * K + 6 * K + 7 * K = 180.
K * (5 + 6 + 7) = 180.
18 * K = 180.
K = 180/18 = 10.
Then the angles of the triangles are equal:
5 * 10 = 50.
6 * 10 = 60.
7 * 10 = 70.
Answer: The largest angle of the triangle is 70.
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