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.
To find the measures of angles a, b, and c, we can start by identifying the relationships between the angles in the figure.
1. The angle opposite to angle a is 30 degrees. Since angles that are opposite each other when two lines intersect are equal, angle a is also 30 degrees.
2. Angle a is the angle of a right triangle, and another angle in a right triangle is b. Therefore, angle b is also 30 degrees.
3. The angle adjacent to angle c is 75 degrees. Since the sum of the angles in a triangle is 180 degrees, we can find angle c by subtracting the given angles from 180 degrees:
Angle c = 180 - 30 - 75
Angle c = 75 degrees
Therefore, the measures of angles a, b, and c are:
Angle a = 30 degrees
Angle b = 30 degrees
Angle c = 75 degrees
no words
Angle a = 30 degrees
Angle b = 30 degrees
Angle c = 75 degrees