Point P is on side AC of the triangle ABC such that angle APB = angle ABP and angle ABC - angle ACB = 49. find PBC in degrees.
Just a bit of algebra will do it.
\(\alpha +2\beta =180\) (1)
\(\alpha +\beta +\delta +\gamma =180\) (2)
\(\beta +\delta -\gamma =49\) (3)
Subtract (2) from (1) to get
\(\beta -\delta -\gamma =0\) (4)
Solvinf (4) for \(\beta -\gamma \) and substituting that in (3) results in
\(\delta +\delta = 2\delta =49\),
which gives you \(\delta =24.5\).
Just a bit of algebra will do it.
\(\alpha +2\beta =180\) (1)
\(\alpha +\beta +\delta +\gamma =180\) (2)
\(\beta +\delta -\gamma =49\) (3)
Subtract (2) from (1) to get
\(\beta -\delta -\gamma =0\) (4)
Solvinf (4) for \(\beta -\gamma \) and substituting that in (3) results in
\(\delta +\delta = 2\delta =49\),
which gives you \(\delta =24.5\).
