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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.

 Jun 16, 2021

Best Answer 

 #1
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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 \(\delta =24.5\).

 Jun 16, 2021
 #1
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+1
Best Answer

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 \(\delta =24.5\).

Guest Jun 16, 2021

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