What is the measure of the angle labeled (5x+42)° ?
2 answers:
These angles are known as alternate interior angles. A fact about them is that they are always congruent. Since they are congruent, we can set them equal to each other:
Let's find the value of x so that we can find what (5x + 42) is:
x = 15 so we can plug that in to find the angle:
Thus, that angle is equal to 117° .
We see two parallel lines crossed by a transversal.
The two labelled angles are alternate interior angles, hence they are equal.
The equality allows us to equate the two expressions and hence solve for x.
8x-3=5x+42
transpose terms
8x-5x=42+3
solve for x
3x=45
so x=45/3=15.
This means 5x+42=5*15+42=75+42=117 degrees.
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