Two angles of a quadrilateral measure 308° and 17°. The other two angles are in a ratio of 3:4. What are the measures of those two angles?
Let's call the two unknown angles x and y. We know that:
- x:y is in a ratio of 3:4, so we can write x = 3a and y = 4a for some value of a.
- The sum of the angles in a quadrilateral is 360°, so we can write an equation:
308° + 17° + x + y = 360°
Substituting in our expressions for x and y, we get:
308° + 17° + 3a + 4a = 360°
Simplifying the left side:
325° + 7a = 360°
Subtracting 325° from both sides:
7a = 35°
Dividing by 7:
a = 5°
So x = 3a = 15° and y = 4a = 20°. Therefore, the two unknown angles are 15° and 20°.
To find the measures of the other two angles in the quadrilateral, we can use the fact that the sum of the angles in a quadrilateral is 360 degrees.
Let's denote the two angles in the ratio of 3:4 as 3x and 4x, where x is a positive number.
We know that the sum of all four angles is 360 degrees, so we can set up the following equation:
308 + 17 + 3x + 4x = 360
Combine like terms:
325 + 7x = 360
Subtract 325 from both sides:
7x = 35
Divide both sides by 7:
x = 5
Now that we have the value of x, we can find the measures of the two angles in the ratio of 3:4:
3x = 3 * 5 = 15 degrees
And
4x = 4 * 5 = 20 degrees
Therefore, the measures of the other two angles in the quadrilateral are 15° and 20°.