A triangle has an angle that measures 26°. The other two angles are in a ratio of 5:6. What are the measures of those two angles?
the angles sum to 180°
So, if the unknown angles are 5x and 6x, we have
26 + 5x + 6x = 180
Solve for x, and then you can get the angles.
To solve this question, we'll first need to find the sum of the measures of the three angles in a triangle, which is always 180 degrees.
Let's call the measures of the other two angles "5x" and "6x" since they are in a ratio of 5:6.
Now we can set up an equation to find the value of "x".
The equation is: 26 + 5x + 6x = 180
Combining like terms, we get: 26 + 11x = 180
Next, we can isolate "x" by subtracting 26 from both sides of the equation:
11x = 180 - 26
Simplifying, we have: 11x = 154
To solve for x, divide both sides of the equation by 11:
x = 154 / 11
Calculating, we find that x is approximately equal to 14.
Finally, we can find the measures of the two angles by substituting the value of x back into the equation:
Angle 1 = 5x = 5 * 14 = 70 degrees
Angle 2 = 6x = 6 * 14 = 84 degrees
Therefore, the measures of the two angles are 70 degrees and 84 degrees.