Practicing Success
If one of the angles of a triangle is 74°, then the angle between the bisectors of the other two interior angles is : |
53° 106° 127° 16° |
127° |
In \(\Delta \)ABC, such that \(\angle\)ACB = \({74}^\circ\) and bisectors \(\angle\)A and \(\angle\)B meet at D and E. Now, In \(\Delta \)ABC, \(\angle\)ACB + \(\angle\)ABC + \(\angle\)BAC = \({180}^\circ\) = \({74}^\circ\) + \(\angle\)ABC + \(\angle\)BAC = \({180}^\circ\) = \(\angle\)ABC + \(\angle\)BAC = \({180}^\circ\) - \({74}^\circ\) = \({106}^\circ\) = \(\frac{1}{2}\)(\(\angle\)ABC + \(\angle\)BAC) = \({53}^\circ\) = \(\angle\)PBA + \(\angle\)BAP = \({53}^\circ\) Now, In \(\Delta \)PAB, \(\angle\)PBA + \(\angle\)BAP + \(\angle\)BPA = \({180}^\circ\) = \({53}^\circ\) + \(\angle\)BPA = \({180}^\circ\) = \(\angle\)BPA = \({180}^\circ\) - \({53}^\circ\) = \({127}^\circ\) Therefore, \(\angle\)BPA = \({127}^\circ\). |