Question

The sides OP and RO of triangle POR are produced to points S and T respectively. If ∠SPR = 145° and ∠POT = 115° , find ∠PRO

Answer 1

`\angle PRQ = 80`

Explanation:

Given

`\angle SPR = 145^o`

`\angle POT = 115^o`

See attachment

Required

Find
`\angle PRO`

First, calculate
`\angle RPO`

`\angle RPO + \angle SPR = 180` --- angle on a straight line

So, we have:

`\angle RPO + 145 = 180`

Collect like terms

`\angle RPO = 180 - 145`

`\angle RPO = 35`

Next, calculate PQR

`\angle POR + \angle POT = 180`

So, we have:

`\angle POR + 115 = 180`

Collect like terms

`\angle POR = 180-115`

`\angle POR = 65`

So, PRO is calculated as:

`\angle PRO + \angle POR + \angle RPO = 180` --- angles in a triangle

So, we have:

`\angle PRO + 65 + 35= 180`

`\angle PRO + 100= 180`

Collect like terms

`\angle PRO = 180-100`

`\angle PRO = 80`