What are the measures of Angles a, b, and c? Show your work and explain your answers. Two straight lines intersect at a point to form angle a. The measure of the angle opposite to angle a is 30 degrees. Angle a is the angle of a right triangle having another angle equal to b. A triangle with one angle labeled c is on the left of the figure. The angle adjacent to c is labeled 75 degrees.
We can start by finding the measure of angles a and b in the right triangle formed by the two intersecting lines.
Since the angle opposite to angle a is 30 degrees, angle a must be equal to 30 degrees.
Since angle a is the angle of a right triangle with another angle equal to b, and the sum of angles in a triangle is 180 degrees, we can calculate angle b as follows:
b = 90 degrees - a
b = 90 degrees - 30 degrees
b = 60 degrees
Therefore, angles a and b have measures of 30 degrees and 60 degrees, respectively.
Next, we focus on the triangle on the left side of the figure. The angle adjacent to angle c is labeled 75 degrees. Since the sum of angles in a triangle is 180 degrees, we can calculate angle c as follows:
c = 180 degrees - 75 degrees
c = 105 degrees
Therefore, angle c has a measure of 105 degrees.