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Angles around a central point measure 21^, 57^, 42^, and 3y. Find the value of y.

May 27, 2026Mathematics

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Answer

y = 80

4 steps

Let's find the value of $y$ .

Identify the type of angles.
The angles $21^\circ$ , $57^\circ$ , $42^\circ$ , and $3y$ are angles around a central point. The sum of angles around a point is $360^\circ$ .
Set up the equation.
Add all the given angles and equate them to $360^\circ$ :
$21^\circ + 57^\circ + 42^\circ + 3y = 360^\circ$
Sum the known angles.
$120^\circ + 3y = 360^\circ$
Solve for $y$ .
Subtract $120^\circ$ from both sides of the equation:
$3y = 360^\circ - 120^\circ$ $3y = 240^\circ$
Divide by 3:
$y = \frac{240^\circ}{3}$ $y = 80^\circ$
The value of $y$ is 80.
$y = 80$

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