Question

Two angles of a quadrilateral measure 290° and 20°. The other two angles are in a ratio of 2:3. What are the measures of those two angles?

° and
°

Answer 1

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 \(30°\).