Question

Please help i dont understand this at all. if you could also elaborate too

Answer 1

∠A = 115°

∠B = 65°

∠C = 115°

∠D = 65°

Explanation:

The figure given is of parallelogram.

We need to find measure of each interior angle.

We are given:

∠A = (2x-15)°

∠B = x°

∠C = (2x-15)°

∠D = x°

We need to find measure of ∠A , ∠B, ∠C, ∠D

We know that sum of all angles of parallelogram = 360°

So, we can write: ∠A +∠B+ ∠C+ ∠D = 360°

Now putting their values and finding value of x first:

`2x-15+x+2x-15+x=360\\Combining\:like\:terms:\\2x+x+2x+x-15-15=360\\6x-30=360\\6x=360+30\\6x=390\\x=(390)/(6)\\x=65`

So, we get x= 65

Now finding measure of each angle:

∠A = (2x-15)° = 2(65)-15 = 130-15 = 115°

∠B = x° = 65°

∠C = (2x-15)° = 2(65)-15 = 130-15 = 115°

∠D = x°= 65°

Answer is:

∠A = 115°

∠B = 65°

∠C = 115°

∠D = 65°