Question

Identify an obtuse angle and give its measure.

Answer 1

DEK is an obtuse angle and the measure is 160 degrees

Answer 2

• ∠DEK = 160°
• ∠FEK = 105°

Explanation:

You want to identify an obtuse angle in the figure, and report its measure.

Obtuse angle

An obtuse angle is one that measures more than 90° and less than 180°. Here, the obtuse angles are recognizable as having one ray horizontal and the other ray in the opposite quadrant.

The measure is found by using the scale for which the protractor reads 0 on the horizontal ray.

DEK

Ray ED is a horizontal ray on the left side of the figure. Ray EK is a (non-horizontal) ray on the right side of the figure. The angle between them is an obtuse angle.

Ray ED crosses the protractor at 0 on the outer scale. Ray EK crosses the protractor at 160 on the outer scale.

The measure of obtuse angle DEK is 160°.

FEH

Ray EF is a horizontal ray on the right side of the figure. Ray EH is a (non-horizontal) ray on the left side of the figure. The angle between them is obtuse.

Ray EF crosses the protractor at 0 on the inner scale. Ray EH crosses the protractor at 105 on the inner scale (at the mark halfway between 100 and 110).

The measure of obtuse angle FEH is 105°.

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Additional comment

Angle KEH is 105-20 = 85 degrees. It is acute.

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