In triangle ABC, angle Bis five less than twice angle A and angle Cis sixty less than angle B. What is the measurment of all of the triangles angles?
To find the measurements of the angles in triangle ABC, we'll need to set up equations based on the given information.
Let's start by assigning variables to the angles:
Let angle A be represented by 'x'.
Angle B will be represented by '2x - 5' (twice angle A minus 5).
And angle C will be represented by '2x - 5 - 60' (angle B minus 60).
In any triangle, the sum of all its angles is always 180 degrees.
Using this information, we can write the equation for triangle ABC as:
x + (2x - 5) + (2x - 5 - 60) = 180.
Now, let's solve for 'x' to find the value of angle A:
x + 2x - 5 + 2x - 5 - 60 = 180.
Combine like terms: 5x - 70 = 180.
Add 70 to both sides: 5x = 250.
Divide by 5: x = 50.
Now that we know x = 50, we can substitute this value back into the expressions for angles B and C.
Angle B = 2x - 5 = 2(50) - 5 = 100 - 5 = 95.
Angle C = 2x - 5 - 60 = 2(50) - 5 - 60 = 100 - 5 - 60 = 35.
Therefore, the measurements of the angles in triangle ABC are:
Angle A = x = 50 degrees.
Angle B = 95 degrees.
Angle C = 35 degrees.