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

12a) Determine the measure of the unknown angle x.-example-1

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Answer:

70°

Explanation:

You want to know the measure of the second acute angle in a right triangle that has one acute angle measuring 20°.

Angle sum theorem

The angle sum theorem tells you the sum of angles in a triangle is 180°. The square box in the corner of this triangle tells you that is a right angle that has a measure of 90°. Then the sum of angles is ...

20° +90° +x = 180°

x = 180° -110° = 70°

The measure of unknown angle x is 70°.

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Additional comment

Since the measure of a right angle is always 90°, the sum of the measures of the two acute angles in a right triangle is 180°-90° = 90°. That is, they are complementary.

x = 90° -20° = 70°

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