Two angles of a quadrilateral measure 316° and 6°. The other two angles are in a ratio of 7:12. What are the measures of those two angles?
We know that the sum of all four angles in a quadrilateral is 360 degrees. We can use this to find the measure of the other two angles:
Let x be the measure of the smaller of the two remaining angles.
Then the larger angle has a measure of (7/12)x, since the two angles are in a ratio of 7:12.
We can now write an equation based on the sum of all four angles:
316° + 6° + x + (7/12)x = 360°
Simplifying the equation:
322° + (19/12)x = 360°
(19/12)x = 38°
x = 24°
So the smaller angle has a measure of 24 degrees, and the larger angle has a measure of (7/12)x24 = 42 degrees.
Therefore, the two remaining angles are 24° and 42°.
To find the measures of the other two angles, let's first calculate the sum of all the angles in the quadrilateral.
We know that the sum of angles in a quadrilateral is always 360 degrees.
Since we have two angle measures, 316 degrees and 6 degrees, the sum of these two angles is 316 + 6 = 322 degrees.
Now, let's find the sum of the other two angles using the given ratio of 7:12.
The ratio 7:12 can be represented as 7x:12x, where x is a common factor.
The sum of these two angles is 7x + 12x = 19x.
Since the sum of all the angles in the quadrilateral is 360 degrees, we have the equation: 322 + 19x = 360.
Simplifying the equation, we have 19x = 360 - 322, which gives us 19x = 38.
Dividing both sides by 19, we get x = 2.
Now, let's find the measures of the other two angles:
Angle 1: 7x = 7 * 2 = 14 degrees.
Angle 2: 12x = 12 * 2 = 24 degrees.
Therefore, the measures of the other two angles are 14 degrees and 24 degrees, respectively.