I'm stuck with these problems! will mark brainliest if you are correct!

(D) -3 < x < 17

Step-by-step explanation:

x must satisfy both Part 1 and Part 2 below:

Part 1:  Length must be greater than 0 so:

2x + 6 > 0       and        x + 23 > 0

       x > -3       and               x > -23

To satisfy both, x > -3

Part 2: The 80° is less than the 100° so the corresponding side of 80° must also be less than the corresponding side of 100°

        80° < 100°

⇒ 2x + 6 < x + 23

      x + 6 <       23

      x       <        17

Therefore x must be between -3 and 17

⇒  -3 < x < 17

(C) -1.6 < y < 7

Step-by-step explanation:

y must satisfy both Part 1 and Part 2 below:

Part 1:  Length must be greater than 0 so:

4y + 15 > 0             and        5y + 8 > 0

         y > -3.75       and               y > -1.6

To satisfy both, y > -1.6

Part 2: The 60° is less than the 105° so the corresponding side of 60° must also be less than the corresponding side of 105°

        60° < 105°

⇒ 5y + 8 < 4y + 15

      y + 8 <        15

      y       <         7

Therefore y must be between -1.6 and 7

⇒  -1.6 < y < 7

(A) 2.4 < y < 5

Step-by-step explanation:

y must satisfy both Part 1 and Part 2 below:

Part 1:  Length must be greater than 0 so:

2y + 3 > 0       and        5y - 12 > 0

       y > -1.5       and               y > 2.4

To satisfy both, y > 2.4

Part 2: The 70° is less than the 140° so the corresponding side of 70° must also be less than the corresponding side of 140°

        70° < 140°

⇒ 5y - 12 < 2y + 3

    3y - 12 <         3

    3y       <        15

      y       <          5

Therefore y must be between 2.4 and 5

⇒  2.4 < y < 5

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step-by-step explanation:

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