Question

M23 is (3x + 4)º and mz5 is (2x + 11)

Answer 1

9514 1404 393

Answer:

• same-side interior
• (3x +4) +(2x +11) = 180
• 77°

Step-by-step explanation:

Angles 3 and 5 are on the same side of the transversal, between the parallel lines, so can be called "same-side interior angles". These are also called "consecutive interior angles". As such, they have a sum of 180°, so are also "supplementary angles." We don't know what your pull-down menu options are, but perhaps one of these descriptions is on there.

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Because the angles are supplementary, their sum is 180°. So, the equation ...

  (3x +4)° +(2x +11)° = 180°

can be used to solve for x. Likewise, any of the possible simplifications of this can be use:

  (3x +4) +(2x +11) = 180 . . . . . divide by degrees

  5x +15 = 180 . . . . . . . . . . . collect terms

  5x = 165 . . . . . . . . . . . . . subtract 15

  x = 33 . . . . . . . . . . . . . . divide by 5

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Once we know that x=33, then the measure of angle 5 is found from its expression:

  m∠5 = (2x +11)° = (2·33 +11)°

  m∠5 = 77°