Answer:
∠A = 115°
∠B = 65°
∠C = 115°
∠D = 65°
Step-by-step 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:
[tex]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=\frac{390}{6}\\x=65[/tex]
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°
