In triangle ABC if angle A-B =42degree and angle B-C =21degree .Find the measures of angles A,B and C
53
To find the measures of angles A, B, and C in triangle ABC, we can use the fact that the sum of the interior angles of a triangle is always 180 degrees.
Given that angle A-B = 42 degrees and angle B-C = 21 degrees, we can find the measure of angle A as follows:
1. Start with the fact that angle A-B + angle B-C + angle C-A = 180 degrees.
2. Substitute the given values into the equation: 42 + 21 + angle C-A = 180.
3. Simplify the equation: angle C-A = 180 - 42 - 21 = 117 degrees.
To find the measure of angle B:
4. Since angle B-C is given as 21 degrees, we can subtract this value from 180 to find angle B: angle B = 180 - 21 = 159 degrees.
Finally, to find the measure of angle C:
5. Substitute the values we have found into the equation angle A + angle B + angle C = 180: 159 + 117 + angle C = 180.
6. Simplify the equation: angle C = 180 - 159 - 117 = 54 degrees.
So, the measures of angles A, B, and C are:
- Angle A = 117 degrees
- Angle B = 159 degrees
- Angle C = 54 degrees.
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.
Given that angle A - B = 42 degrees and angle B - C = 21 degrees, we can start by expressing each angle in terms of a common variable.
Let's say angle A = x.
Using the given information, we can then say angle B = x - 42 degrees, and angle C = x - 42 degrees - 21 degrees.
Now, we can write an equation to represent the sum of the angles in triangle ABC:
x + (x - 42) + (x - 42 - 21) = 180
Simplifying the equation:
x + x - 42 + x - 63 = 180
Combining like terms:
3x - 105 = 180
To solve for x, we can move -105 to the other side of the equation:
3x = 180 + 105
3x = 285
Dividing both sides by 3:
x = 95
Now that we have found the value of x, we can substitute it back into the expressions for angle B and C to find their measures.
Angle B = x - 42
= 95 - 42
= 53 degrees
Angle C = x - 42 - 21
= 95 - 42 - 21
= 32 degrees
Therefore, the measures of angles A, B, and C in triangle ABC are:
Angle A = 95 degrees
Angle B = 53 degrees
Angle C = 32 degrees
A-B=42
B-C=21
A+B+C=180
now just solve the 3 equations