In an isosceles triangle the measure of the vertex angle is (x+3)^circ . The measures of the b are (3x+1)^circ and (4y+4)^circ , respectively. What is the measure of the vertex angle of the isosceles triangle? A. 28^circ B. 47^circ C. 76^circ D. 104^circ

## Step 1: Setting up the equation### Since the triangle is isosceles, two of its angles must be equal. We are given that the base angles are and . Therefore, we can set up the equation .## Step 2: Solving for x in terms of y### Subtract 1 from both sides of the equation: . Then, divide both sides by 3: .## Step 3: Using the triangle sum theorem### The sum of the angles in a triangle is . So, . Simplifying, we get , or . Dividing by 4, we get .## Step 4: Substituting x and solving for y### Substitute into : . Multiply both sides by 3: . Combine like terms: . Subtract 3 from both sides: . Divide by 7: .## Step 5: Solving for x### Substitute into : . Subtract 18 from both sides: .## Step 6: Finding the vertex angle### The vertex angle is . Substitute : .