A quadrilateral has two angles that measure 270° and 68°. The other two angles are in a ratio of 4:7. What are the measures of those two angles?
We know that the sum of the angles in a quadrilateral is 360 degrees. We can use this fact to find the measure of the other two angles.
Let's call the measure of one of the angles x. Then the measure of the other angle is 11x/4 (since the two angles are in a ratio of 4:7).
We can set up an equation:
270 + 68 + x + 11x/4 = 360
Multiplying both sides by 4 to get rid of the fraction, we get:
1080 + 272 + 4x + 11x = 1440
Simplifying, we get:
15x = 88
x = 88/15
So one of the angles is approximately 5.87 degrees.
To find the measure of the other angle, we can plug x back into our equation:
11x/4 = 11(88/15)/4 = 22.53 degrees
Therefore, the two angles are approximately 5.87 degrees and 22.53 degrees.
To find the measures of the other two angles, we need to use the fact that the sum of all angles in a quadrilateral is equal to 360°.
1. Let's start by subtracting the two given angles from 360° to find the total measure of the other two angles combined.
360° - 270° - 68° = 22°
2. We are given that the other two angles are in a ratio of 4:7. Let's assume the common ratio is x.
So, the measure of the first angle is 4x, and the measure of the second angle is 7x.
3. Now, we can set up an equation based on the ratio and the total measure of the other two angles:
4x + 7x = 22°
4. Combining like terms, we have:
11x = 22°
5. To solve for x, divide both sides of the equation by 11:
x = 22° / 11
x = 2°
6. Now that we have the value of x, we can find the measures of the other two angles:
Measure of the first angle = 4x = 4(2°) = 8°
Measure of the second angle = 7x = 7(2°) = 14°
Therefore, the measures of the other two angles are 8° and 14°.