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

Answer:

Option C is correct

The value of y is, $44^{\circ}$

Step-by-step 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, $44^{\circ}$