Question

12b) Determine the measure of the unknown angle x.

Answer 1

x = 65°

Explanation:

Step 1: Determine the sum of the measures of the polygon:

• The Polygon Interior Angle Sum Theorem states that the sum of the interior angles of a polygon with n sides is equal to 180(n - 2)°.

Thus, we plug in 4 for n to find the sum of the interior angles of this four-sided polygon:

Sum = 180(4 - 2)

Sum 180 * 2

Sum = 360

Thus, the sum of the interior angles of this four-sided polygon is 360°.

Step 2: Find x by setting the sum of the interior angles equal to 360°:

Setting the sum of the interior angles of the four-sided polygon equal to 360 will allow us to find the measure of x:

x + 110 + 105 + 80 = 360

x + 295 = 350

x = 65

Thus, x = 65°

Answer 2

65°

Explanation:

You want the measure of the angle marked x in a quadrilateral with the other angles marked as 110°, 105°, and 80°.

Sum of angles

The sum of the interior angles of a quadrilateral is 360°. Using that relation, we have ...

x + 110° +105° +80° = 360°

x = 360° -295° = 65°

The measure of angle x is 65°.

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Additional comment

If the sum of adjacent angles is 180°, then the sides of the figure are parallel. That is not the case here, so this figure is not a trapezoid.

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