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 degree
Known Interior angle + unknown interior angle + right angle = 180
70 + 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]
