Please answer my question step be step

9514 1404 393

  z = 20

  m∠A = 70°

Step-by-step explanation:

Step 0: read and understand the question. Identify the given information and the information requested.

Step 1: consult your knowledge of inscribed quadrilaterals to determine that opposite angles are supplementary.

Step 2: identify angles A and C as being marked with expressions in z.

Step 3: use those expressions and the relation in Step 1 to write an equation.

  A + C = 180°

  (4z -10)° +(10 +5z)°= 180°

Step 4: solve for z.

  9z = 180 . . . . simplify, divide by °

  z = 20 . . . . . . divide by 9

Step 5: use the relation between z and the measure of angle A to answer the question.

  m∠A = (4z -10)° = (4·20 -10)°

  m∠A = 70°

Step 6: check your answer. This can be done by making sure that angle C is supplementary to angle A.

  C = (10 +5z)° = (10 +5·10)° = 110° = 180° -70° ∴ answer checks OK

you answer is a

step-by-step explanation: