Question

the triangle below models a section of the supports you might see in a construction crane. a. what is the sum of the angle measures of the triangle? show your work. 180 use calculator 30 + 60+90 = 180 solution b. check your answer to problem 3a. show your work. 142 lesson 7 describe angle relationships in triangles downloaded by r. brown. this resource expires on 6/30/2024.

Explanation:

Step1: Recall angle - sum property

The sum of the interior angles of any triangle is always 180 degrees. In the given right - triangle, one angle is 60 degrees and another is 90 degrees. The third angle can be found using the fact that the sum of angles in a triangle is 180 degrees. Let the third angle be $x$. Then $x + 60+90 = 180$. Solving for $x$, we get $x=180-(60 + 90)=30$ degrees. And $30+60 + 90=180$.

Step2: Check the answer

We know that the angle - sum property of a triangle is a well - established geometric fact. For any triangle, the sum of its interior angles must equal 180 degrees. In our case, we have calculated the sum of the three angles ($30^{\circ},60^{\circ},90^{\circ}$) as 180 degrees, which is consistent with the angle - sum property of triangles.

Answer:

a. 180 degrees
b. The sum of the interior angles of a triangle is always 180 degrees. We have found the three angles of the triangle to be 30 degrees, 60 degrees, and 90 degrees, and $30 + 60+90=180$ degrees, which verifies our answer for part a.