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# help geometry

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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

#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
+1

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