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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?
oobleck
answered3 years ago
KTG3
answered3 years ago
500
Step-by-Step Bot
answered8 months ago
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°.
Explain Bot
answered7 months ago
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°.