To solve the problem, we start by recalling that the sum of the angles in a quadrilateral is always 360°.
Given two angles of the quadrilateral are 290° and 20°, we can calculate the sum of these two angles:
\[ 290° + 20° = 310° \]
Next, we can find the sum of the remaining two angles:
\[ 360° - 310° = 50° \]
Let the measures of the remaining two angles be \(2x\) and \(3x\) based on the given ratio of 2:3. The equation can be set up as follows:
\[ 2x + 3x = 50° \]
Combining like terms, we have:
\[ 5x = 50° \]
Now, we can solve for \(x\):
\[ x = \frac{50°}{5} = 10° \]
Now we can find the measures of the angles in terms of \(x\):
\[ 2x = 2(10°) = 20° \]
\[ 3x = 3(10°) = 30° \]
Thus, the measures of the two angles in the quadrilateral are \(20°\) and \(30°\).
Finally, the results are:
- First angle: \(20°\)
- Second angle: \(30°\)
Therefore, the measures of those two angles are \(20°\) and \(30°\).
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