The exterior angle at C if a triangle is ABC IS =120 degree find the measure of all the angles of a triangle if angle A= angle B
C=180-120=60
so, since B=A,
A+A=60 = 180
...
To find the measure of all the angles of a triangle when given the measure of one exterior angle and the fact that two angles are equal, you can follow these steps:
1. Recall that the sum of the measures of the interior angles of a triangle is always 180 degrees.
2. Let's label the exterior angle at C as angle X.
3. Since the exterior angle and its corresponding interior angle (angle C) form a straight line, they sum up to 180 degrees. Therefore, angle C = 180 degrees - X.
4. We are given that angle A = angle B. Let's call this measure angle Y.
5. Since the sum of the interior angles of a triangle is 180 degrees, we have: angle A + angle B + angle C = 180 degrees.
6. Replacing the known angles with their measures, we get: Y + Y + (180 - X) = 180 degrees.
7. Simplifying the equation, we have: 2Y + (180 - X) = 180 degrees.
8. Combining similar terms, we have: 2Y - X = 0.
9. Now, let's use the fact that the sum of all three angles in a triangle is 180 degrees to solve for the value of angle Y.
10. Angle Y + angle Y + angle C = 180 degrees.
11. Replacing the known angles with their measures, we have: Y + Y + (180 - X) = 180 degrees.
12. Simplifying the equation, we have: 2Y + (180 - X) = 180 degrees.
13. Combining similar terms, we have: 2Y - X = 0.
14. Since we know from the problem statement that the exterior angle at C is 120 degrees, we have: 2Y - 120 = 0.
15. Solving for Y, we have: 2Y = 120 degrees.
16. Dividing both sides by 2, we get: Y = 60 degrees.
17. Now that we know angle Y is 60 degrees, we can substitute it back into the equation for angle C: 180 - X = 60 degrees.
18. Solving for X, we have: X = 180 - 60 degrees.
19. Simplifying, we get: X = 120 degrees.
20. Finally, to find angle A and angle B, since we are given that they are equal, we know they both measure 60 degrees.
Therefore, the measure of all the angles of the triangle is angle A = angle B = angle Y = 60 degrees, and angle C = angle X = 120 degrees.