The angles of a triangle are in AP (arithmetic progression). If measure of the smallest angle is 50° less than that of the largest angle, then find the largest angle (in degrees).

85

Let the smallest angle of the triangle be \({(A \;-\;D)}^\circ\)

Now,

The second largest angle of the triangle = \({A}^\circ\)

The largest angle of the triangle = \({(A \;+\;D)}^\circ\)

According to the question,

\({(A \;+\;D)}^\circ\) - \({50}^\circ\) = \({(A \;-\;D)}^\circ\)

= \({(A \;+\;D)}^\circ\) - \({(A \;-\;D)}^\circ\) = \({50}^\circ\)

= 2D = \({50}^\circ\)

= D = \({25}^\circ\)

Now,

\({(A \;-\;D)}^\circ\) + \({(A \;+\;D)}^\circ\) + \({A}^\circ\) = \({180}^\circ\)

= \({3A}^\circ\) = \({180}^\circ\)

= \({A}^\circ\) = \({60}^\circ\)

The largest angle of the triangle = \({(A \;+\;D)}^\circ\) = (60 + 25) = \({85}^\circ\)

Therefore, The largest angle of the triangle is  \({85}^\circ\).