Question

Two congruent, isosceles triangles are joined to create a parallelogram. the largest angle of the parallelogram is 116.

write two equations
solve them to find the value of a and b

Answer 1

Yes very much so good job

Answer 2

4 a + 2b = 360 ----->equation 1

a + b = 116 --------> equation 2

a = 64 °

b = 52°

Explanation:

The sum of all of the internal angles would be 360°. Since we have four "a"s and two "b"s, we have:

4a + 2b = 360

Then told that the largest internal angle of the parallelogram is 116 degrees, so:

a + b = 116

We now have a system of two equations and two unknowns.

I'll simplify the first equation by dividing both sides by 2, then multiplying the second equation by -1 to prepare for solving by elimination:

2a + b = 180

-a - b = -116

---------------------- Add the equations together to get:

a = 64°

Now we can solve for b:

a + b = 116

64 + b = 116

b = 52°

So the values of "a" and "b" are:

a = 64° and b = 52°

Hope this helped :)