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.

a =64 °and b = 52°

Step-by-step 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°

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

4

step-by-step explanation: