Triangle ABC has the angle measures shown. Measure of angle A = (2 x) degrees. Measure of angle B = (3 x) degrees. Measure of angle C = (4 x) degrees. Which statement is true about the angles? Measure of angle A = 20 degrees Measure of angle B = 60 degrees Angle A and Angle B are complementary Measure of angle A + measure of angle C = 100 degrees
The Correct Answer and Explanation is:
Let’s break down the given problem:
We have a triangle ABC, where:
- Measure of angle A = (2x) degrees
- Measure of angle B = (3x) degrees
- Measure of angle C = (4x) degrees
The sum of the interior angles of any triangle is always 180 degrees. Therefore, we can write the equation for the sum of the angles in triangle ABC:Angle A+Angle B+Angle C=180\text{Angle A} + \text{Angle B} + \text{Angle C} = 180Angle A+Angle B+Angle C=180
Substitute the expressions for the angles:2x+3x+4x=1802x + 3x + 4x = 1802x+3x+4x=180
Now, solve for xxx:9x=1809x = 1809x=180x=1809=20x = \frac{180}{9} = 20x=9180=20
Now that we have the value of x=20x = 20x=20, let’s calculate the actual measures of the angles:
- Measure of angle A = 2x=2×20=402x = 2 \times 20 = 402x=2×20=40 degrees
- Measure of angle B = 3x=3×20=603x = 3 \times 20 = 603x=3×20=60 degrees
- Measure of angle C = 4x=4×20=804x = 4 \times 20 = 804x=4×20=80 degrees
Evaluating the Statements:
- Measure of angle A = 20 degrees – This is incorrect. The measure of angle A is 40 degrees, not 20 degrees.
- Measure of angle B = 60 degrees – This is correct. From the calculation, we find that the measure of angle B is indeed 60 degrees.
- Angle A and Angle B are complementary – Two angles are complementary if their sum is 90 degrees. Here, the sum of angle A (40 degrees) and angle B (60 degrees) is 100 degrees, not 90, so this is incorrect.
- Measure of angle A + measure of angle C = 100 degrees – This is incorrect. The sum of angle A (40 degrees) and angle C (80 degrees) is 120 degrees, not 100 degrees.
Conclusion:
The correct statement is “Measure of angle B = 60 degrees”.
