Given A and B are vertical angles with m ∠A = 20x + 10 and m ∠B =30x - 10, the value of x is 2
From the Vertical angle theorems, we have that
Two opposite vertical angles formed when two lines intersect each other are always equal to each other.
Now, from the question, we are given that A and B are vertical angles
That means
A = B
Also, from the question
measure of angle A = 20x + 10 and measure of angle B = 30x - 10
To determine the value of x, we will equate the two equations to each other
A = 20x + 10
B = 30x - 10
Since, A = B
∴ 20x + 10 = 30x - 10
To solve for x,
20x + 10 + 10 = 30x - 10 +10
We get
20x + 20 = 30x
20x - 20x + 20 = 30x - 20x
20 = 10x
That is,
10x = 20
∴ x = 20 ÷ 10
x = 2
Hence, given A and B are vertical angles with m ∠A = 20x + 10 and m ∠B =30x - 10, the value of x is 2
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