Question

The vertex angle of an isoceles triangle measures (a+15) ° and one of the base angles measures 7a °. Find a and each angle measure.

Answer 1

Keep in mind that:

• the sum of the interior angles of every triangle in existence is 180 degrees
• the base angles of isosceles triangles are congruent

With this information, I have created a diagram. I encourage you to always draw a diagram when you can - it aids in the solving process.

Now, to find a, set the measures of the interior angles equal to 180.

(a + 15) + 7a + 7a = 180

Solve for a.

a + 15 + 7a + 7a = 180

15 + 15a = 180

15a = 165

a = 11

Find the angle measures by plugging 11 for a.

a + 15

(11) + 15

26

7a

7(11)

77

Check your work by adding the angles measures.

77 + 77 + 26 = 180

Answer:

a = 11

Each base angle measures 77 degrees and the vertex angle measures 26 degrees.