 If the angles of a polygon are 90°, 4y°, 100°, 120° and (7y-34°). Find the value of y


The sum of the interior angles of a polygon can be calculated using the formula:

\[
\text{Sum of interior angles} = (n - 2) \times 180^\circ
\]

where \(n\) is the number of sides of the polygon.

In this case, there are 5 angles given, so the polygon is a pentagon. Thus:

\[
\text{Sum of interior angles} = (5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
\]

The angles of the pentagon are \(90^\circ\), \(4y^\circ\), \(100^\circ\), \(120^\circ\), and \( (7y - 34^\circ)\). Adding these together, we get:

\[
90^\circ + 4y^\circ + 100^\circ + 120^\circ + (7y - 34^\circ) = 540^\circ
\]

Simplifying this equation:

\[
90 + 100 + 120 - 34 + 4y + 7y = 540
\]

\[
276 + 11y = 540
\]

Now, solve for \(y\):

\[
11y = 540 - 276
\]

\[
11y = 264
\]

\[
y = \frac{264}{11} = 24
\]

Thus, the value of \(y\) is \(24\).

Would you like further clarification or details?

Here are some related questions:
1. What is the sum of interior angles of a hexagon?
2. How would the equation change if the polygon had 6 sides?
3. Can a polygon have interior angles summing to 360 degrees?
4. What is the measure of the largest angle in this pentagon?
5. How do exterior angles relate to interior angles in a polygon?

**Tip:** Always verify that the total sum of angles matches the polygon's formula to ensure correct calculations.

If the angles of a polygon are 90°, 4y°, 100°, 120° and (7y-34°), find the value of y.

Solve a polygon problem where the angles are 90°, 4y°, 100°, 120°, and (7y-34°). Using the interior angle sum theorem and algebra, we find the value of y step-by-step. Suitable for Grades 8-10.

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