M07.C-G.2.1.2
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 40 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 65 degrees.
To solve for the measures of angles a, b, and c, we first need to understand the relationships between the angles in the figure described.
1. Angle a and the angle opposite to it (let's call it x) form a straight line, so they add up to 180 degrees. Since the measure of x is 40 degrees, we can solve for angle a:
a + x = 180
a + 40 = 180
a = 140 degrees
2. Angle b is the remaining angle in the right triangle with angles a and b. The sum of the interior angles of a triangle is always 180 degrees, so we can solve for angle b:
a + b + 90 = 180
140 + b + 90 = 180
b = 180 - 140 - 90
b = 50 degrees
3. Angle c and the angle adjacent to it (let's call it y) form a straight line, so they add up to 180 degrees. Since the measure of y is 65 degrees, we can solve for angle c:
c + y = 180
c + 65 = 180
c = 180 - 65
c = 115 degrees
Therefore, the measures of angles a, b, and c are 140 degrees, 50 degrees, and 115 degrees, respectively.