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).
Answer & explanation
Correct answer: option 2
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 \({85}^\circ\).