2angles of a quadrilateral are 70 degrees and 110 degrees.The other 2 are in the ratio 4:5.Find these angles.

the angles sum to 360º

360 - 110 - 70 = 180

4n + 5n = 180

find n , then find the two angles (4:5)

To find the other two angles, let's assume the angles in the ratio 4:5 are x and y.

Now, we can set up an equation based on the information given. The sum of the interior angles of a quadrilateral is always 360 degrees.

Given:
Angle 1 = 70 degrees
Angle 2 = 110 degrees
Angle 3 = x degrees
Angle 4 = y degrees

We can now write the equation:
70 + 110 + x + y = 360

Simplifying the equation:
180 + x + y = 360

Now, let's work with the ratio. We know that the two angles are in the ratio 4:5. This means that x:y = 4:5. We can rewrite this as:
x = (4/5) * y

Substituting this value of x in the equation:
180 + (4/5)y + y = 360

Combining like terms:
180 + (9/5)y = 360

To solve for y, we can subtract 180 from both sides to isolate y:
(9/5)y = 180
y = (5/9) * 180

Calculating y:
y = 100

Now, substitute the value of y back into the equation for x:
x = (4/5) * 100
x = 80

Therefore, the other two angles of the quadrilateral are:
Angle 3 = 80 degrees
Angle 4 = 100 degrees