Two angles of a quadrilateral measure 39° and 61°. The other two angles are in a ratio of 6:7. What are the measures of those two angles?
Let x be the smaller angle and y be the larger angle. Then we know:
x + y + 39° + 61° = 360° (the sum of the angles in a quadrilateral is 360°)
x + y = 260°
We also know that y/x = 7/6, which means y = (7/6)x.
Substituting this into the first equation, we get:
x + (7/6)x = 260°
(13/6)x = 260°
x = 120°
Therefore, y = (7/6)x = (7/6)(120°) = 140°.
The two missing angles are 120° and 140°, in a ratio of 6:7.
To find the measures of the other two angles, we can set up an equation using the given ratio of 6:7.
Let's denote the measures of the other two angles as 6x and 7x.
Since a quadrilateral has a total of 360 degrees, we can set up the equation:
6x + 7x + 39 + 61 = 360
Combining like terms, we have:
13x + 100 = 360
Subtracting 100 from both sides, we get:
13x = 260
Dividing both sides by 13, we find:
x = 20
Now, we can substitute x back into our equation to find the measures of the other two angles:
1st angle: 6x = 6(20) = 120 degrees
2nd angle: 7x = 7(20) = 140 degrees
Therefore, the measures of the other two angles in the quadrilateral are 120 degrees and 140 degrees.