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Damm [24]
2 years ago
11

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

Mathematics
1 answer:
Margarita [4]2 years ago
3 0

Answer:

\angle PRQ = 80

Step-by-step 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

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