Question

LESSON 7 SESSION 1 1 3 The triangle below models a section of the supports you might see in a construction crane. 2 3/60° 4 5 a. What is the sum of the angle measures of the triangle? Show your work.

Answer 1

EXPLANATION

Since this is a triangle, we can assevere by the alternate interior angles postulate that the angles 4 is of 90 degrees.

Then, by the Triangle Interior Angles Theorem, we know that the sum of the interior angles is equal to 180 degrees.

Thus,

60 + 4 + 2 = 180

As 4= 90

60 + 90 + m∠2 = 180

Isolating m∠2:

m∠2 = 180 - 90 - 60

Subtracting terms:

m∠2 = 30

Then, we know that the angles ∠1, ∠2 and right angle are complementary.

By definition, the sum of complementary angles is equal to 90 degrees.

Thus,

m∠1 + m∠2 = 90

Substituting terms:

m∠1 + 30 = 90

Isolating m∠1:

m∠1 = 90 - 30 = 60

Then, we know that the angles 60 and 3 are supplementary, so their sum is equal to 180°

So,

m∠3 + 60 = 180

Isolating m∠3:

m∠3= 180 - 60 = 120

Finally, we have that the angles 4 and 5 are the same measure because they are supplementary angles.

m∠4=m∠5 = 90

The measure of all the angles are:

m∠1= 60°

m∠2= 30°

m∠3= 120°

m∠4=90°

m∠5=90°