Question

Two congruent, isosceles triangles are joined, as shown, to form a parallelogram.

The largest angle of the parallelogram is 116º.

Write two equations.

Solve them to find the value of a and the value of b.

Answer 1

a =64 °and b = 52°

Explanation:

as 360° is the sum of all the internal angles.

As we have 4 a's and 2 b's.(see attachment for the figure).

We write the equation:

4 a + 2b = 360 ---> eq(1)

We are given that the largest angle of the parallelogram is 116º.

So a + b = 116

a= 116-b ---> eq(2)

substituting the above value in eq(1)

(1) => 4( 116-b) + 2b = 360

464 - 4b + 2b = 360

-2b = 360- 464

-2b = -104

b=52

plugging the value of b in eq (2)

(2)=>

a= 116- 52

a= 64

Thus, the values of a is 64 °and b is 52°