1. The angle ∠SUT is composed of two adjacent angles, ∠1 and ∠2.
2. Therefore, the measure of ∠SUT equals the sum of the measures of ∠1 and ∠2: m∠SUT = m∠1 + m∠2.
3. The problem states that m∠2 = 18x - 1 and m∠SUT = 34x.
4. From the diagram, it is evident that ∠1 and ∠2 are equal (indicated by the same arc mark on both angles). So, m∠1 = m∠2 = 18x - 1.
5. Substitute the expressions into the equation from step 2:
34x = (18x - 1) + (18x - 1)
6. Simplify the right side:
34x = 36x - 2
7. Subtract 34x from both sides:
0 = 2x - 2
8. Add 2 to both sides:
2 = 2x
9. Divide both sides by 2:
x = 1
10. The correct answer is C) 1.
Parent Tip: Review the logic above to help your child master the concept of triangle angle bisector worksheet.
