Question

Calculate the size of the angles that have letters

Answer 1

a=67°

b=64°

c=113°

Explanation:

180=49+64+a

a=67

Alternate interior angles are congruent

b=64

49+64=c

113=c

Answer 2

• a = 67°
• b = 64°
• c = 113°

Explanation:

Linear Pair: Two or more angles that are supplementary and form a straight line. In other words, the sum of the measures of the two or more angles is 180 degrees.

So,

we can say that:

64° + 49° + a = 180° (linear pair)

Simplify like terms:

113° + a = 180°

Subtract 113° on both sides:

113° + a - 113° = 180° - 113°

a = 67°

`\hrulefill`

Alternate Interior Angles: Alternate interior angles are pairs of angles formed by a transversal intersecting two parallel lines. They are congruent, meaning they have the same measure.

So,

we can say that:

b = 64° (alternate interior angles)

`\hrulefill`

Co-interior Angles: Co-interior angles are pairs of angles formed by a transversal intersecting two lines and lying on the same side of the transversal. They are supplementary, meaning their sum is 180 degrees.

So,

we can say that:

c + a = 180° (co-interior angles)

Substitute value of a.

c + 67° = 180°

Subtract 67° on both sides:

c + 67° -67°= 180° - 67°

c = 113°

Therefore, the values of angles a, b, and c are:

• a = 67° (linear pair)
• b = 64° (alternate interior angles)
• c = 113° (co-interior angles)