Angles and Algebra
In the diagram, ray AB bisects ∠SAT. The measures of the two congruent angles are (x + 20)° and 2x - 10)°. Solve for x.
Any time you see a variable in a geometry problem you must set up an equation to solve for the variable. Look for anything that equals to something that is true to that problem. In our problem we know an angle bisector splits the large angle into two congruent angles. This means that each angle is "equal" to each other. Now we can use this fact to set up the equation as follows: m∠SAB = m∠___
Answer: BAT
∠SAT= ∠BAT
Solve for x.
Now, substitute in the values given for angles from the diagram.
___ + ___ = 2x - 10
Answer: x, 20
Subtract x from each side.
Answer: 30 = x
In the diagram, AL bisects ∠EAT. The measures of the two congruent angles are (3x - 5)° and (x + 45)°.
Solve for x.
∠EAL = ∠___
Answer: LAT
Substitute the measures of the angles.
3x___ = ___ + 45
Answer: 5, x
Subtract x from both sides to isolate it.
___ - 5 = ___
Answer: 2x, 45
So x = ___
Answer: 25
