The angles of a triangle are x, y and 40^(@). The difference between the two angles x and y is 30^(@). Find x and y.

Triangle Angle Sum Equation: The sum of the angles in any triangle is 180 degrees. We can write this as an equation: x + y + 40 = 180Difference Between Angles: We also know that the difference between angles x and y is 30 degrees. We can express this as another equation: x - y = 30Solving System of Equations: Now we have a system of two equations with two variables: 1) x + y + 40 = 180 2) x - y = 30 We can solve this system by using the substitution or elimination method. Let's use the elimination method by adding the two equations together to eliminate y. (x + y + 40) + (x - y) = 180 + 30Adding Equations: Simplifying the equation, we get: 2x + 40 = 210Solving for x: Now, we solve for x by subtracting 40 from both sides of the equation: 2x = 210 - 40 2x = 170Substitute x to Find y: Divide both sides by 2 to find the value of x: x = 170 / 2 x = 85Final Solution: Now that we have the value of x, we can find y by substituting x back into one of the original equations. Let's use the second equation: x - y = 30 85 - y = 30Solve for y by adding y to both sides and subtracting 30 from both sides: y = 85 - 30 y = 55

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The angles of a triangle are x, y and 40^(@). The difference between the two angles x and
y is 30^(@). Find x and y.

The angles of a triangle are $x, y$ and $40^{\circ}$ . The difference between the two angles $x$ and $y$ is $30^{\circ}$ . Find $x$ and $y$ .

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Q. The angles of a triangle are

x, y

and

40^{\circ}

. The difference between the two angles

x

and

y

30^{\circ}

. Find

x

and

y

Triangle Angle Sum Equation: The sum of the angles in any triangle is $180$ degrees. We can write this as an equation: $\newline$ $x + y + 40 = 180$
Difference Between Angles: We also know that the difference between angles $x$ and $y$ is $30$ degrees. We can express this as another equation: $\newline$ $x - y = 30$
Solving System of Equations: Now we have a system of two equations with two variables: $\newline$ $1$ ) $x + y + 40 = 180$ $\newline$ $2$ ) $x - y = 30$ $\newline$ We can solve this system by using the substitution or elimination method. Let's use the elimination method by adding the two equations together to eliminate $y$ . $\newline$ $(x + y + 40) + (x - y) = 180 + 30$
Adding Equations: Simplifying the equation, we get: $2x + 40 = 210$
Solving for x: Now, we solve for $x$ by subtracting $40$ from both sides of the equation: $\newline$ $2x = 210 - 40$ $\newline$ $2x = 170$
Substitute $x$ to Find $y$ : Divide both sides by $2$ to find the value of $x$ :
$x = \frac{170}{2}$
$x = 85$
Final Solution: Now that we have the value of $x$ , we can find $y$ by substituting $x$ back into one of the original equations. Let's use the second equation: $\newline$ $x - y = 30$ $\newline$ $85 - y = 30$
Final Solution: Now that we have the value of $x$ , we can find $y$ by substituting $x$ back into one of the original equations. Let's use the second equation: $\newline$ $x - y = 30$ $\newline$ $85 - y = 30$ Solve for $y$ by adding $y$ to both sides and subtracting $30$ from both sides: $\newline$ $y = 85 - 30$ $\newline$ $y = 55$