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Which of the following is a true statement about the angles in the figure below?

Which of the following is a true statement about the angles in the figure below?-example-1
User Mike Minicki
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1 Answer

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20 votes

Answer:

The statement which is true about the angles in the figure is;

The measure of Angle 4 is 137 degrees

Explanation:

From the question diagram, we have;

The interior angles of the triangle are;

43°, 56°, and ∠1

Therefore, by the angle sum theorem, we have;

∠1 = 180° - 43° - 56° = 81°

∠1 = 81°

The measure of ∠1 is 81°

By the sum of angles on a straight line, we have;

∠1 + ∠2 = 180°

∴ 81° + ∠2 = 180°

∠2 = 180° - 81° = 99°

The measure of ∠2 is 99°

Similarly, for the angles 56° and ∠3 which are on a straight line, we have;

56° + ∠3 = 180°

∠3 = 180° - 56° = 124°

The measure of ∠3 is 124°

For the angles 43° and ∠4 which are on a straight line, we have;

43° + ∠4 = 180°

∠4 = 180° - 43° = 137°

The measure of ∠4 is 137°

Therefore the true statement is the measure of angle 4 is 137 degrees.

User Rockwell
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