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Please help me with this

Please help me with this-example-1
User Jack Guy
by
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1 Answer

22 votes
22 votes

Answer:

  • y = 13
  • z = 14

Explanation:

You want the values of y and z in the figure showing a triangle with exterior angle 135° opposite remote interior angles (5y+5)° and (4z+9)°, where angle (4z+9)° is adjacent to exterior angle (9y-2)°.

Exterior angle

The exterior angle of a triangle is equal to the sum of the remote interior angles. This can be used to find both y and z.

The lower left interior angle is 180° -135° = 45°, so the right-side exterior angle is ...

(9y -2)° = (5y +5)° +45°

4y = 52 . . . . . . . . . . . . . divide by °, add 2-5y

y = 13 . . . . . . . . . . divide by 4

The lower left exterior angle is ...

135° = (5y +5)° +(4z +9)°

135 = 5(13) +5 +4z +9 . . . . . . . . . divide by °, substitute value of y

56 = 4z . . . . . . . . . . . . . . . . subtract 79

14 = z . . . . . . . . . . . . divide by 4

The values of y and z are 13 and 14, respectively.

User Fabricio Colombo
by
2.5k points