Question

The angles of a triangle are 40°, 60°, 80° and a circle touches its sides at P, Q, R, calculate the angles of triangle PQR?

I don't understand what the diagram will look like

Answer 1

See explanation.

Explanation:

recall that tangent segments to a circle from an external point are equal in length,
`=> AP=AR, BP=BQ, and CQ=CR`,
`=> DeltaAPR, DeltaBPQ and DeltaCQR` are isosceles triangles.
`=> angleAPR=angleARP=(180-40)/2=70^@`
similarly, `angleBPQ=angleBQP=(180-60)/2=60^@`
similarly, `angleCQR=angleCRQ=(180-80)/2=50^@`
`=> angleRPQ=180-70-60=50^@`
`anglePQR=180-60-50=70^@`
`anglePRQ=180-70-50=60^@`

Footnote : `DeltaBPQ` is actually an equilateral triangle.