2 intersecting lines create 4 angles with the same vertex labelled A, B, C, D. angle B is adjacent to angle A and C. find angle A if angle C = 75
Since angles A, B, C, and D are all formed by intersecting lines, the sum of the angles at the same vertex must equal 360 degrees.
Therefore, we can write the equation:
Angle A + Angle B + Angle C + Angle D = 360
We know that angle C = 75 degrees, so substituting this in gives us:
Angle A + Angle B + 75 + Angle D = 360
As angle B is adjacent to angle A and angle C, angle B + angle A + angle C must equal 180 degrees because they are forming a straight line. Substituting this in gives us:
180 + 75 + Angle D = 360
255 + Angle D = 360
Angle D = 105
Now we know that angle D = 105 degrees, we can substitute this back into the equation we had before to solve for angle A:
Angle A + Angle B + 75 + 105 = 360
Angle A + Angle B = 180
We know that angle B + angle A = 180 degrees, so this tells us that angle A = 180 - angle B.
Since angle D is adjacent to angle B and C, angle D + angle B + angle C must equal 180 degrees because they are forming a straight line. Substituting in the values gives us:
105 + angle B + 75 = 180
Angle B = 180 - 105 - 75
Angle B = 180 - 180
Angle B = 0
Therefore, angle A = 180 - angle B = 180 - 0 = 180 degrees.
So, angle A = 180 degrees.