Question

How can I find missing angles mark by letters in this parallelogram?

Answer 1

In a parallelogram, the opposite angles are congruent. This means they have the same measure. So, we have:

h = 45º

and

i = g

Also, all the four angles must sum up to 360º:

45º + h + i + g = 360º

45º + 45º + i + i = 360º

90º + 2i = 360º

Now, we can solve this equation by applying the same operations on both sides of the equation, until we isolate the variable i and find its value:

90º + 2i = 360º

90º + 2i - 90º = 360º - 90º

2i = 270º

2i/2 = 270º/2

i = 135º

Finally, since g is congruent to i, we have:

g = i = 135º

Therefore, the angles are:

h = 45º

i = 135º

g = 135º