In an isosceles triangle ABis congruent to BC. Measure of angle A is x +3y and the measure of angle C is 3x +2y. The measure of angle C is 63 degrees. Find x and y.
To find the values of x and y, we need to solve the equation for angle C:
3x + 2y = 63
Since we are given that angle A and angle C are congruent, we can also write an equation for angle A:
x + 3y = 63
Now we have a system of two equations with two variables. We can solve this system using the method of substitution or elimination.
Let's solve this system using the substitution method.
1. Solve one of the equations for x in terms of y.
From the equation x + 3y = 63, we can isolate x:
x = 63 - 3y
2. Substitute the expression for x in terms of y into the other equation.
Substituting x = 63 - 3y into the equation 3x + 2y = 63, we have:
3(63 - 3y) + 2y = 63
3. Simplify and solve for y.
Distributing 3 to both terms within the parentheses, we get:
189 - 9y + 2y = 63
Combining like terms, we have:
-7y + 189 = 63
Subtracting 189 from both sides:
-7y = 63 - 189
-7y = -126
Dividing both sides by -7:
y = 18
4. Substitute the value of y back into one of the original equations to solve for x.
Let's use the equation x + 3y = 63:
x + 3(18) = 63
x + 54 = 63
Subtracting 54 from both sides:
x = 63 - 54
x = 9
Therefore, x = 9 and y = 18, which are the values that satisfy the given conditions.