triangle abc angle A+B=166 degree and angle b+c=126 degree find the measure of each angle of the triangle
To find the measures of angles A, B, and C in triangle ABC, we can use the fact that the sum of the angles in any triangle is always 180 degrees.
We are given that angle A + angle B = 166 degrees and angle B + angle C = 126 degrees.
Let's solve for angle A first:
Angle A + Angle B = 166 degrees
Subtracting angle B from both sides: Angle A = 166 degrees - angle B
Next, we'll solve for angle C:
Angle B + Angle C = 126 degrees
Subtracting angle B from both sides: Angle C = 126 degrees - angle B
Now, we have expressions for angles A (166 degrees - angle B) and C (126 degrees - angle B). Using the fact that the sum of angles in a triangle is 180 degrees, we can set up an equation:
Angle A + Angle B + Angle C = 180 degrees
Substituting the expressions we found for angle A and angle C:
(166 degrees - angle B) + Angle B + (126 degrees - angle B) = 180 degrees
Simplifying the equation gives:
166 degrees + 126 degrees - 2* angle B = 180 degrees
Combining like terms:
292 degrees - 2* angle B = 180 degrees
Subtracting 292 degrees from both sides:
-2* angle B = -112 degrees
Dividing both sides by -2:
angle B = 112 degrees / 2
angle B = 56 degrees
Now that we know angle B is 56 degrees, we can substitute it back into the expressions for angle A and angle C to find their measures:
Angle A = 166 degrees - angle B = 166 degrees - 56 degrees = 110 degrees
Angle C = 126 degrees - angle B = 126 degrees - 56 degrees = 70 degrees
So, the measures of angles A, B, and C in triangle ABC are 110 degrees, 56 degrees, and 70 degrees respectively.
Very bad solution
#boka
your third equation is
a+b+c = 180
now just solve the system as usual.