The acute angles of a right-angled triangle are 2: 7. What are these angles equal to?
July 8, 2021 | education
| Let’s denote by x half the size of the smaller of the acute angles of the given right-angled triangle.
Then the value of the smaller of the acute angles of the given right-angled triangle should be equal to 2x.
According to the condition of the problem, the acute angles of a right-angled triangle are 2: 7, therefore, the value of the largest of the acute angles of this right-angled triangle should be equal to 7x.
Since the sum of the angles of each triangle is 180 °, we can write the following equation:
2x + 7x + 90 = 180,
solving which, we get:
9x + 90 = 180;
9x = 180 – 90;
9x = 90;
x = 90/9 = 10.
Find sharp corners:
2 * 10 = 20 °;
7 * 10 = 70 °.
Answer: 20 ° and 70 °.
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