One angle of a triangle measures 125°. The other two angles are in a ratio of 5:6. What are the measures of those two angles?
125 + 5x + 6x = 180
500
Let's call the measure of the first angle x.
The other two angles are in a ratio of 5:6.
So, the measures of the other two angles can be represented as 5x and 6x.
The sum of the angles of a triangle is always 180°.
Therefore, we can write the equation as: x + 5x + 6x = 180.
Simplifying the equation, we get: 12x = 180.
Dividing both sides of the equation by 12, we find: x = 15.
So the measure of the first angle is 15°.
The measure of the second angle is 5x, which is equal to 5 * 15 = 75°.
The measure of the third angle is 6x, which is equal to 6 * 15 = 90°.
Therefore, the measures of the other two angles are 75° and 90°.
To find the measures of the other two angles, we need to first find the total sum of all three angles in the triangle.
The total sum of all angles in a triangle is always 180°.
Given that one angle measures 125°, we can subtract this angle from 180° to find the sum of the other two angles:
180° - 125° = 55°
Now we need to find the actual measures of the other two angles in the ratio of 5:6.
To do this, we can set up an equation. Let's assume the measure of the smaller angle (in the 5:6 ratio) is 5x°, and the measure of the larger angle is 6x°.
According to the ratio, we know that:
5x° + 6x° = 55°
Combining like terms:
11x° = 55°
Now we can solve for x by dividing both sides of the equation by 11:
11x° / 11 = 55° / 11
x° = 5°
Now that we know x, we can find the actual measures of the other two angles:
5x° = 5 * 5° = 25°
6x° = 6 * 5° = 30°
Therefore, the measures of the other two angles in the triangle are 25° and 30°.