Answer:
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°
