ABCD is an isosceles trapezoid. mAngle SymbolABC= 3x+10 and mAngle SymbolBAD=4x-5. Solve for x.
The sum of ABC and BAD is 180 degrees.
7x + 5 = 180
x = 25 degrees.
To solve for x, we need to use the properties of an isosceles trapezoid. In an isosceles trapezoid, the base angles (angles adjacent to the parallel sides) are congruent.
Given that ABCD is an isosceles trapezoid, we have two base angles: angle ABC and angle BAD. These angles are congruent, so we can set up an equation:
m∠ABC = m∠BAD
Substituting the given values:
3x + 10 = 4x - 5
Now, we can solve for x by isolating it on one side of the equation. Let's solve it step by step:
3x + 10 = 4x - 5
Let's get rid of the terms with x on one side by subtracting 3x from both sides of the equation:
3x - 3x + 10 = 4x - 3x - 5
Simplifying:
10 = x - 5
Next, let's isolate x by getting rid of the constant term on the same side as x. Add 5 to both sides of the equation:
10 + 5 = x - 5 + 5
Simplifying:
15 = x
So, x is equal to 15.