The three angles of a triangle are x°,
(x + 30)° , (x – 6)° . Find the dimension of each angle.
Miscellaneous Problem
4.) The three angles of a triangle are x , ( x+30), (x-6)
The sum of the angle of a triangle is 180.
x + (x + 30) + (x-6) = 180
x + x + 30 + x – 6 = 180
3x + 30 – 6 = 180
3x + 24 = 180
3x = 180 – 24
3x = 156
x = 52 degree
(x + 30) degree
52 + 30 = 82 degree
and
(x – 6) degree
52 – 6 = 46 degree
Isn't the sum of all 3 angles equal to 180°
well. .....
To find the dimensions of each angle in a triangle, you can use the fact that the sum of the angles in a triangle is always 180 degrees.
So, we can set up an equation using the given angles:
x + (x + 30) + (x - 6) = 180
Now, let's solve for x.
Combine like terms:
3x + 24 = 180
Subtract 24 from both sides:
3x = 156
Divide both sides by 3:
x = 52
Now that we have the value of x, we can substitute it back into the expressions for each angle to find their dimensions.
Angle 1: x° = 52°
Angle 2: (x + 30)° = 52° + 30° = 82°
Angle 3: (x - 6)° = 52° - 6° = 46°
So, the dimensions of the three angles are 52°, 82°, and 46°.