Q1. The three angles of a triangle measure (2x-10°),(x+31°) and (5x+7°). Find the value of x and hence all three angles of the triangle
Q2. A father's age is three times as his old son. 15 years hence, he will be twice as old as his son. What is the sum of their present ages?
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Q1. The three angles of a triangle measure (2x-10°), (x+31°), and (5x+7°). Find the value of x and hence all three angles of the triangle.
In a triangle, the sum of all three angles is always 180°. We can set up an equation based on this principle:
(2x-10°) + (x+31°) + (5x+7°) = 180°
Combine like terms:
8x + 28° = 180°
Subtract 28° from both sides:
8x = 152°
Divide by 8:
x = 19°
To find the values of all three angles, substitute the value of x back into each expression:
Angle 1: 2x - 10° = 2(19°) - 10° = 38° - 10° = 28°
Angle 2: x + 31° = 19° + 31° = 50°
Angle 3: 5x + 7° = 5(19°) + 7° = 95° + 7° = 102°
Therefore, the three angles of the triangle are 28°, 50°, and 102°.
Q2. A father's age is three times as old as his son. 15 years hence, he will be twice as old as his son. What is the sum of their present ages?
Let's denote the son's age as x. According to the given information, the father's age is three times that of his son, so the father's age would be 3x.
After 15 years, the son's age will be x + 15 and the father's age will be 3x + 15. According to the second statement, the father's age will be twice that of his son's age, so we can set up the equation:
3x + 15 = 2(x + 15)
Simplify and solve for x:
3x + 15 = 2x + 30
3x - 2x = 30 - 15
x = 15
The son's age is x = 15, and the father's age is 3x = 3(15) = 45.
The sum of their present ages is 15 + 45 = 60 years.