A building makes a 90° angle with the ground. A ladder leans against the building, making a 110° exterior angle with the ground. What are the measures of the two interior angles?

Accepted Solution

Answer:A building makes a [tex]90^{\circ}[/tex] angle with the ground .The two interior angles are [tex]70^{\circ}[/tex] and [tex]20^{\circ}[/tex]Solution: Given, a ladder which is against the building wall makes an exterior angle of [tex]110^{\circ}[/tex]And building makes a  [tex]90^{\circ}[/tex] angle with the ground.So, altogether it makes a right angle triangle with ladder as hypotenuse and ground as base leg and building as another leg.   Now, we know that, sum of exterior angles and interior angles equals to [tex]180^{\circ}[/tex]Here, in the case of ground and ladder, exterior angle is [tex]110^{\circ}[/tex] and interior angle is unknown.Exterior angle + interior angle = 180 110 + interior angle = 180 Interior angle = 180 – 110 Interior angle = [tex]70^{\circ}[/tex]We have found one of the two interior angles of right angle triangle.We know that, sum of angles in a triangle is 180 degreeKnown Interior angle + unknown interior angle + right angle = 18070 + unknown interior angle + 90 = 180 Unknown interior angle + 160 = 180 Unknown interior angle = 180 - 160 Unknown interior angle = [tex]20^{\circ}[/tex]Hence the two interior angles are  [tex]70^{\circ}[/tex] and [tex]20^{\circ}[/tex]