Question

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?

Answer 1

Answer: A building makes a 90 degrees angle with the ground .The two interior angles are 70 and 20 degrees

Explanation:

Answer 2

A building makes a
`90^(\circ)` angle with the ground .The two interior angles are
`70^(\circ)` and
`20^(\circ)`

Solution:

Given, a ladder which is against the building wall makes an exterior angle of
`110^(\circ)`

And building makes a
`90^(\circ)` 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
`180^(\circ)`

Here, in the case of ground and ladder, exterior angle is
`110^(\circ)` and interior angle is unknown.

Exterior angle + interior angle = 180

110 + interior angle = 180

Interior angle = 180 – 110

Interior angle =
`70^(\circ)`

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 =
`20^(\circ)`

Hence the two interior angles are
`70^(\circ)` and
`20^(\circ)`