Question

Given that point S is the incenter of right triangle PQR and angle RQS is 30°, what are the measures of angles RSQ and RPQ?

Answer 1

see explanation.

Explanation:

Recall that the three angle bisectors of a triangle meet at the incenter of the triangle, and given that `angleRQS=30^@`,
`=> anglePQR=30xx2=60^@`,
a) case 1 : see Fig 1,

if `DeltaPQR` is right angled at `R`,
`=> angleRPQ=180-90-60=30^@`
`=> angleRSQ=180-45-30=105^@`

b) case 2: see Fig 2,

if `DeltaPQR` is right angled at `P`,
`=> angleRPQ=90^@`
`=> anglePRQ=180-60-90=30^@`
`=> angleRSQ=180-15-30=135^@`