Used to triangle song t h e o r e m to find a measure of each angle for the triangle shown in a diagram eight time plus 5°, five-time - 1° four time plus six degrees A 50°, 54°, and 93° B 42°, 44° and 79° c 46°, 49° and 85°, d 46° 50° and 85°
To solve this problem, we can use the Triangle Sum Theorem, which states that the sum of the angles in a triangle is always 180°.
Let's denote the measures of the angles in the triangle as follows:
Angle 1 = 8t + 5°
Angle 2 = 5t - 1°
Angle 3 = 4t + 6°
Using the Triangle Sum Theorem, we can write the equation:
Angle 1 + Angle 2 + Angle 3 = 180°
Substituting the values from above, we get:
(8t + 5°) + (5t - 1°) + (4t + 6°) = 180°
Combining like terms, we have:
17t + 10° = 180°
Next, we can solve for t:
17t = 170°
t = 10°
Now that we have the value of t, we can substitute it back into the expressions for the angles:
Angle 1 = 8t + 5° = 8(10°) + 5° = 80° + 5° = 85°
Angle 2 = 5t - 1° = 5(10°) - 1° = 50° - 1° = 49°
Angle 3 = 4t + 6° = 4(10°) + 6° = 40° + 6° = 46°
Therefore, the measure of each angle in the triangle is 85°, 49°, and 46°.
So the correct answer is option C: 46°, 49°, and 85°.