finding the measure

Question

a geodesic dome is consumed of two different types of triangular panels. one of these is an isosceles triangle . in one geodesic dome , the measure of the third angle is 82.5 more than the measure of either of the two equal angles find the measure of the three angles

Answer 1

In an isosceles triangle, the two base angles are congruent.

The sum of the angles (in any triangle) equal 180 degrees. Let...

 

          x = measure of each base angle (2 thus)

x+82.5 = measure of 3rd angle

 

x+x+(x+82.5)=180.......measure of two base angles plus 3rd

                                      angle equal 180 degrees

         3x+82.5=180......combine like terms

                  3x=97.5.....subtract 82.5, both sides

                ∴ x=32.5.....divide both sides by 3

 

      32.5+82.5=115......measure of 3rd angle, substitute for "x"

 

So the measure of the angles of the triangle are...

32.5º, 32.5° (base angles) and 115° (3rd angle)

 

Let's check...

32.5+32.5+115=180

                  180=180....√check, our solution is correct

 

Always check your work and solution!