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Answer:
x=6
Step-by-step explanation:
Kindly look at the image provided below.
The image shows the relationship between intersecting secants and their corresponding arcs which is important to understand when looking at problems like these.
The relationship states that an angle formed by two intersecting secants is equal to half the sum of its corresponding arc and its vertical angles corresponding arc.
So ∠FHG = 1/2 ( arc FG + arc EB )
* substitute the given expressions for each angle and arc *
we would then have
15x - 2 = 1/2 ( -2 + 12x + 16x + 10 )
We now solve for x
Step 1 multiply each side by 2
1/2 ( -2 + 12x + 16x + 10 ) *2 = ( the 2 and 1/2 cancels out ) -2 + 12x + 16x + 10
(15x - 2 )2 = 30x - 4
we now have -2 + 12x + 16x + 10 = 30x - 4
step 2 combine like terms
-2 + 10 = 8
12x + 16x = 28x
now we have 30x - 4 = 28x + 8
step 3 add 4 to each side
-4 + 4 cancels out
8 + 4 = 12
Now we have 30x = 28x + 12
step 4 subtract 28x from each side
30x - 28x = 2x
28x - 28x cancels out
now we have 2x = 12
step 5 divide each side by 2
2x / 2 = x
12 / 2 = 6
we're left with x = 6
