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.

the correct answer is

Angle a:

Vertical angles are equal.

a = 30°

Angle b:

(ΔABC). In a triangle, the three interior angles always add to 180°.

90° + 30° + b = 180° ⇒ 120° + b = 180° ⇒ b = 180° - 120° ⇒ b = 60°.

Angle c:

Angles on one side of a straight line will always add to 180 degrees.

c + 75° = 180° ⇒ c = 180° - 75° ⇒ c = 105°.

Look at the picture.

Angle a:

Vertical angles are equal.

a = 30°

Angle b:

(ΔABC). In a triangle, the three interior angles always add to 180°.

90° + 30° + b = 180° ⇒ 120° + b = 180° ⇒ b = 180° - 120° ⇒ b = 60°.

Angle c:

Angles on one side of a straight line will always add to 180 degrees.

c + 75° = 180° ⇒ c = 180° - 75° ⇒ c = 105°.

[tex]What are the measures of angles a, b, and c? show your work and explain your answers. two straight[/tex]

Since angle a is on the opposite side of an angle with a known measure of 30º, that means angle a is vertical to it, and vertical angles both have the same measurement.

So angle a is 30º.

Since angle a and b are in a right triangle, that means we know 2 angles from that triangle and can find angle b.

Since the right triangle has a measure of 90º in its corner and we know angle a is 30º, we can add 30º and 90º then subtract this from 180º to get the measure of angle b, since all triangles' angles add up to 180º.

30 + 90 = 120

180 - 120 = 60

So angle b is 60º.

Angle c is a supplementary angle with the known angle of 75º.

Supplementary angles are angles that add up to 180º and form a straight line.

To find angle c, just subtract 75º from 180º.

180 - 75 = 105

So angle c is 105º.

Answers:

Angle A- 30º

Angle B- 60º

Angle C- 105º