Question

In a triangle ABC, $\angle ABC={150}^{\circ }$ and P is the orthocenter of $△ABC$. Find the value of $\angle APC$

Answer 1

REF.Image

Orthocenter is the point where perpendicular

from there vertices to the three sides

of a triangle meet.

Here perpendicular from A and C to

BC and AB produced meet at P.

As $\angle ABM+\angle ABC={180}^{\circ }$

$\Rightarrow \angle ABM={30}^{\circ }$

In $△ABM,\angle AMB+\angle ABM+\angle MAB={180}^{\circ }$

${90}^{\circ }+{30}^{\circ }+\angle MAB={180}^{\circ }$

$\Rightarrow \angle MAB={60}^{\circ }$

In $△APL,\angle APL+\angle ALP+\angle PAL={180}^{\circ }$

$\Rightarrow \angle APL+{90}^{\circ }+{60}^{\circ }={180}^{\circ }\Rightarrow \angle APL=\angle APC={30}^{\circ }$