Respuesta :

Answer:

66 degrees.

Step-by-step explanation:

angle 4 is 124, and angle 1 and 4 make 180 degrees. that means angle 1 is 56 degrees (180-124). and the total angle in a triangle is also 180 degrees.

Add 56 and 58, you'd get 114.

180-114=66

angle 2=66 degrees.

renknee

Answer:

66

Step-by-step explanation:

1. The exterior angle theorem states that the measure of an exterior angle of a triangle is congruent to the sum of the two opposite interior angles.

  • Basically, exterior angle = opposite interior angle + opposite interior angle

2. Now, let's see what information we have so far, and what we don't have.

  • m∠4 is 124 degrees, is the exterior angle
  • The angle with 58 degrees is one of the opposite interior angles
  • ∠2 is the other opposite interior angle, but we don't know its measure

3. Now, let's set up the equation and solve it.

Step 1: Set up the equation.

  • [tex]124 = x + 58[/tex]

Step 2: Subtract 58 from both sides.

  • [tex]124-58=x+58-58[/tex]
  • [tex]66 = x[/tex]

Step 3: Check if solution is correct.

  • [tex]124=66+58[/tex]
  • [tex]124=124[/tex]

Therefore, the answer is 66.

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