Question

Triangle WXY has the interior and exterior angles shown below.

Triangle X W Y. Angle W is (2 x minus 13) degrees and angle Y is x degrees. The exterior angle to angle X is 122 degrees.

What is Measure of angle W?
45 degrees
58 degrees
68 degrees
77 degrees

Answer 1

77 is the answer

Explanation:

Answer 2

The correct option is last one 77 degrees.

Therefore the measure angle W is 77 degrees.

Explanation:

Given:

Exterior angle = 122°

∠W = (2x-13)°

∠Y= x°

To Find:

∠W = (2x-13)° = ?

Solution:

Exterior Angle Property:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Angle W and Angle Y are the interior angles of Exterior angle 122°.

∴
`Exterior\ angle=m\angle W+m\angle Y`

Substituting the values we get

`122=2x-13+x\\3x=135\\\\x=(135)/(3)=45\\\\x=45`

Now Substitute 'x' in angle W we get

`m\angle W=2* 45 -13=77\°`

Therefore the measure angle W is 77 degrees.