A right triangle has acute angles measuring 2x+6 degrees and 3x−26 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle. Do you know the answer? explain how you got it
To find the missing angles of a triangle, we can use the Triangle Angle Sum Theorem, which states that the sum of the three interior angles of a triangle is always 180 degrees.
Let's denote the measures of the two given acute angles as A and B.
A = 2x + 6
B = 3x - 26
To find the third angle, we subtract the sum of angles A and B from 180 degrees:
C = 180 - (A + B)
C = 180 - (2x + 6 + 3x - 26)
C = 180 - 5x - 20
C = 160 - 5x
Therefore, the measure of the missing angle is 160 - 5x degrees.
Without knowing the specific values of x, we cannot determine the exact measures of the missing angles. However, we can express them in terms of x as shown above.
can you break it down a bit more? i still dont follow. i am sorry
No problem! I'll break it down step by step for you.
1) Let's denote the measures of the two given acute angles as A and B:
A = 2x + 6 (first angle)
B = 3x - 26 (second angle)
2) According to the Triangle Angle Sum Theorem, the sum of the three interior angles of a triangle is always 180 degrees. So, we can represent this as an equation:
A + B + C = 180
3) We need to find the measure of the missing angle, which we'll call C. To do this, we can rearrange the equation from step 2 to solve for C:
C = 180 - (A + B)
4) Substitute the values of A and B from step 1 into the equation for C:
C = 180 - (2x + 6 + 3x - 26)
5) Simplify the expression inside the parentheses:
C = 180 - (5x - 20)
6) Distribute the negative sign to each term inside the parentheses:
C = 180 - 5x + 20
7) Combine like terms:
C = 200 - 5x
Therefore, the measure of the missing angle, C, is 200 - 5x degrees.
With this equation, you can find the measure of angle C by plugging in the value of x. Without knowing the specific value of x, we cannot determine the exact measure of angle C.