Question

What is the value of y ?

Answer 1

Theorem:
In a triangle, the measure of an exterior angle is equal to the sum of the measures of the remote interior angles.

The 88-deg angle is an exterior angle of the triangle.
The two angles labeled y are the remote interior angles to the 88-deg angle.

That means that the sum of the measures of the angles labeled y equals 88.

y + y = 88

2y = 88

y = 44

Answer: C. 44 deg

Answer 2

Option C is correct

The value of y is,
`44^(\circ)`

Explanation:

Exterior Angle theorem states that the sum of the measures of the two non-adjacent interior angles of the triangle is equal to the measure of an exterior angle.

Label the figure:

In triangle ABC, BC is produced to D, then
`\angle ACD` is the exterior angle ,
`\angle ABC` and
`\angle BAC` are the two interior opposite angle.

i.e,
`\angle ABC+\angle BAC=\angle ACD`

From the given figure:

`\angle ABC = \angle BAC = y^(\circ)` and
`\angle ACD`
`=88^(\circ)`

Then, by the Exterior angle theorem, we calculate the value of y;

`y^(\circ)+y^(\circ)=88^(\circ)`

Combine like terms:

`2y^(\circ)=88^(\circ)`

on simplify:

`y=44^(\circ)`

therefore, the value of y is,
`44^(\circ)`