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
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.
3 answers
no words
Angle a = 30 degrees
Angle b = 30 degrees
Angle c = 75 degrees
Angle b = 30 degrees
Angle c = 75 degrees