Triangle MNO ~ triangle PRQ. If

89o

69o

79o

99o

The measure of angle R is 99° ⇒ Last answer

Step-by-step explanation:

In similar triangles

Corresponding angles are equal in measures Corresponding sides are proportion

∵ Δ MNO is similar to Δ PRQ

∴ m∠M = m∠P

∴ m∠N = m∠R

∴ m∠O = m∠Q

In Δ MNO

∵ m∠M = 23°

∵ m∠O = 58°

- The sum of the measures of the interior angles of a Δ is 180°

∵ m∠M + m∠N + m∠O = 180°

∴ 23 + m∠N + 58 = 180

- Add the like terms in the left hand side

∴ 81 + m∠N = 180

- Subtract 81 from both sides

∴ m∠N = 99°

∵ m∠R = m∠N ⇒ proved up

∴ m∠R = 99°