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Sides `B C ,\ C A\ a n d\ B A` of a triangle `A B C` are produced to `D ,\ Q ,\ P` respectively as shown in Figure. If `/_A C D=100^0a n d\ /_Q A P=35^0,` find all the angles of the triangle.

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Solution
`/_QAP = /_BAC = 25@`
By exterior angle theorem,
`/_ACD = /_BAC + /_ABC`
`100^@= 35^@ + /_ABC`
`/_ABC = 100^@ - 35^@`
`/_ABC = 65^@`
`/_BCA + /_ACD = 180^@` [ Linear Pair]
`/_BCA +100^@ = 180^@`
`/_BCA = 80^@`.
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