Given a right-angled triangle ABC with a right angle C, find angle A if angle B is greater than angle A by 40 degrees.
September 20, 2021 | education
| By the condition of the problem, the angle C is straight, which means it is equal to 90 degrees. By the property of triangles – the sum of all the angles of a triangle is 180 degrees. Let the angle A be equal to x, then the angle B is equal to (x + 40), we will compose the expression:
x + (x + 40) + 90 = 180.
Move the numerical values to the right, leaving the unknown on the left and solve:
x + x = 180 – 40 – 90
2x = 50
x = 50/2
x = 25
Angle A is 25 degrees, then angle B: 25 + 40 = 65 degrees.
You can easily check the correctness of the solution:
25 + 65 + 90 = 180 degrees.
Answer: Angle A is 25 degrees.
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