A quadrilateral has two angles that measure 150° and 80°. The other two angles are in a ratio of 4:9. What are the measures of those two angles?
150+80 + 4x+9x = 360
x=10
so the angles are 40° and 90°
PLEASE HELP
To find the measures of the other two angles of the quadrilateral, we need to first determine the total sum of the angles in a quadrilateral.
A quadrilateral has four angles, and the sum of its angles is always 360 degrees.
So, to find the measures of the other two angles, we need to subtract the sum of the given angles from 360 degrees.
Given:
Angle 1 = 150°
Angle 2 = 80°
Sum of given angles = 150° + 80° = 230°
Now, subtract the sum of the given angles from 360 degrees:
360° - 230° = 130°
So, the sum of the other two angles is 130 degrees.
Next, we are given that the other two angles are in a ratio of 4:9.
Let's assign variables to the two angles:
Let the first angle be 4x.
Let the second angle be 9x.
According to the ratio, the sum of the two angles is 130 degrees:
4x + 9x = 130°
Combining like terms:
13x = 130°
Divide both sides of the equation by 13:
x = 10°
Now, substitute the value of x back into the expressions for the angles:
First angle = 4x = 4 * 10° = 40°
Second angle = 9x = 9 * 10° = 90°
So, the measures of the other two angles are 40° and 90°.