If m∠4 = 2x + 5 and m∠8 = x + 75, what is the value of x?
a.50
b.60
c.65
d.70
Answers
The value of x is option (d). 70°.
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Let's understand a few concepts:
To solve the value of x we first need to understand the concept of the corresponding angles.
What are corresponding angles?
When a transversal line cuts at least two parallel lines, then a pair of congruent angles are formed on the same side of the transversal. These angles are known as corresponding angles.
These angles can also be recognised in the shape of "F".
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Let's solve the given problem:
Here we have
The measure of ∠4 = (2x + 5)°
The measure of ∠8 = (x + 75)°
From the figure, we can say that
∠4 and ∠8 are forming the F-shape angles i.e., ∠4 corresponds to ∠8
⇒ ∠4 and ∠8 are the corresponding angles
Therefore, we get,
m∠4 = m∠8
⇒ (2x + 5)° = (x + 75)°
⇒ 2x° - x° = 75° - 5°
⇒ x° = 70° ← option (d)
Thus, the value of x is 70°.
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