Find the scale factor of the figures. Then list all pairs of congruent angles. DEFG∼PQRS

k=

9514 1404 393

  k = 1/3

  ∠D ≅ ∠P

  ∠E ≅ ∠Q

  ∠F ≅ ∠R

  ∠G ≅ ∠S

Step-by-step explanation:

The scale factor is the ratio of corresponding side lengths. It is convenient to choose one of the sides that has length 1.

  k = QR/EF

  k = 1/3

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Corresponding angles are listed in the same order by the similarity statement.

  ∠D ≅ ∠P

  ∠E ≅ ∠Q

  ∠F ≅ ∠R

  ∠G ≅ ∠S

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°