Question

Lamar wanted to explain why the measure of angle 5 is equal to the sum of the measures of angles 1 and 3. A triangle with angles 1, 2, 3. The exterior angle to angle 1 is 4, to 2 is 5, to 3 is 6. Which geometry concepts should be used in Lamar’s work? supplementary angles and the sum of the measures of interior angles of a triangle complementary angles and the sum of the measures of interior angles of a triangle supplementary angles and vertical angles the sum of the measures of interior angles of a triangle and vertical angles.

Answer 1

Lamar explains it correctly. Then the angle ∠5 is equal to the sum of angles ∠1 and ∠2.

What is an angle?

Angle is the space between the line or the surface that meets.  And the angle is measured in degree. For complete 1 rotation, the angle is 360 degrees.

Lamar wanted to explain why the measure of angle 5 is equal to the sum of the measures of angles 1 and 3.

A triangle with angles 1, 2, 3. The exterior angle to angle 1 is 4, to 2 is 5, to 3 is 6.

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

∠2 + ∠5 = 180° ...1

Triangle - The sum of the angle of the triangle is 180 degrees.

∠1 + ∠2 + ∠3 = 180° ...2

From equations 1 and 2, we have

∠2 + ∠5 = ∠1 + ∠2 + ∠3

        ∠5 = ∠1 + ∠3

Thus, angle ∠5 is equal to the sum of angles ∠1 and ∠2.

More about the angled link is given below.

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