If two intersecting lines create four angles with the same vertex labeled a b c and d. Angle b is adjacent to angle a and angle c. Find angle a if angle is 75 degrees
If angle b is adjacent to angle a and angle c, then angle b + angle a + angle c = 180 degrees (since they form a straight line).
Given that angle b is 75 degrees, we can substitute this value into the equation:
75 + angle a + angle c = 180
angle a + angle c = 180 - 75
angle a + angle c = 105
Since angle b is adjacent to angle d and angle c, we can also say angle c + angle d + angle b = 180 degrees.
So, angle c + angle d = 180 - 75 (substituting angle b with 75)
angle c + angle d = 105
Now, if we combine equations:
angle a + angle c = 105
angle c + angle d = 105
Since angle a and angle d are on opposite sides of the straight line, they are supplementary angles. This means angle a + angle d = 180 degrees.
Substituting the values into the equation:
angle a + angle d = 180
angle a + 105 = 180
angle a = 75
Therefore, angle a is 75 degrees.