The first angle of quadrilateral is 50 degree, the second angle is twice the first, and the third angle is equal to the second. What is the measure of the fourth angle?

In a quadrilateral, the sum of the interior angles is always \(360^\circ\). 

You are given the following information about the angles:

1. The first angle is \(50^\circ\).
2. The second angle is twice the first, so it is \(2 \times 50 = 100^\circ\).
3. The third angle is equal to the second, so it is also \(100^\circ\).

Now, we can calculate the fourth angle by subtracting the sum of the first three angles from \(360^\circ\):

\[
\text{Sum of the first three angles} = 50^\circ + 100^\circ + 100^\circ = 250^\circ
\]
\[
\text{Fourth angle} = 360^\circ - 250^\circ = 110^\circ
\]

Thus, the measure of the fourth angle is \(110^\circ\).

Would you like further details or have any questions?

Here are 5 related questions for further exploration:

1. What is the sum of the interior angles of a pentagon?
2. If a quadrilateral has two right angles, what could the other two angles be?
3. How do you determine the sum of interior angles for any polygon?
4. Can a quadrilateral have all angles equal? If yes, what is it called?
5. What is the exterior angle sum of a quadrilateral?

**Tip:** Always remember that the sum of the interior angles of a polygon with \(n\) sides is given by the formula \((n-2) \times 180^\circ\).

Learn how to calculate the fourth angle of a quadrilateral when given that the first angle is 50°, the second angle is twice the first, and the third angle equals the second. This problem applies geometry concepts and the sum of interior angles formula, suitable for Grades 6-8.

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