Find angles A, C. B 50° 4x+10 C 8x A
The Correct Answer and Explanation is:
To solve for angles A and C in the triangle, we will use the fact that the sum of the angles in any triangle is 180°.
Given:
- Angle B = 50°
- Angle A = 8x (where x is a variable)
- Angle C = 4x + 10
Step 1: Use the sum of angles in a triangle
We know that the sum of all angles in a triangle is 180°. Therefore, we can write: Angle A+Angle B+Angle C=180°\text{Angle A} + \text{Angle B} + \text{Angle C} = 180°Angle A+Angle B+Angle C=180°
Substitute the given values for angles A, B, and C: 8x+50+(4x+10)=1808x + 50 + (4x + 10) = 1808x+50+(4x+10)=180
Step 2: Simplify the equation
8x+50+4x+10=1808x + 50 + 4x + 10 = 1808x+50+4x+10=180 12x+60=18012x + 60 = 18012x+60=180
Step 3: Solve for x
Subtract 60 from both sides: 12x=12012x = 12012x=120
Now, divide both sides by 12: x=10x = 10x=10
Step 4: Calculate the angles
- Angle A = 8x = 8 * 10 = 80°
- Angle C = 4x + 10 = 4 * 10 + 10 = 40 + 10 = 50°
Conclusion:
- Angle A = 80°
- Angle C = 50°
