Respuesta :

Answer:

m∠RQS = 102

m∠TQS = 78

Step-by-step explanation:

m∠RQS = (20x + 2)°

m∠TQS = (15x + 3)°

m∠RQS + m∠TQS = 180°

20x + 2 + 15x + 3 = 180

35x + 5 = 180

35x = 175

x = 5

m∠RQS = 20(5) + 2 = 100 + 2 = 102

m∠TQS = 15(5) + 3 = 75 + 3 = 78

Space

Answer:

m∠RQS = 102°

m∠SQT = 78°

General Formulas and Concepts:

Definition of a Line: A line is 180°

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Set up equation

m∠RQS and m∠SQT must add up to m∠RQT.

m∠RQS + m∠SQT = m∠RQT

(20x + 2) + (15x + 3) = 180

Step 2: Solve for x

  1. Combine like terms:                         35x + 5 = 180
  2. Subtract 5 on both sides:                35x = 175
  3. Divide 35 on both sides:                  x = 5

Step 3: Find m∠RQS

  1. Define:                    m∠RQS = 20x + 2
  2. Substitute:              m∠RQS = 20(5) + 2
  3. Multiply:                  m∠RQS = 100 + 2
  4. Add:                        m∠RQS = 102°

Step 4: Find m∠SQT

  1. Define:                    m∠SQT = 15x + 3
  2. Substitute:              m∠SQT = 15(5) + 3
  3. Multiply:                  m∠SQT = 75 + 3
  4. Add:                        m∠SQT = 78°

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