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What is the value of y ?

What is the value of y ?-example-1
User Searock
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2 Answers

2 votes
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
User Uzoma
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6.1k points
3 votes

Answer:

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)


What is the value of y ?-example-1
User Gnosis
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6.2k points