Question

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Answer 1

9514 1404 393

Answer:

• x = 30
• y = 105
• z = 75

Step-by-step explanation:

You know the linear pair z° and 105° are supplementary angles, so ...

  z = 180 -105 = 75

The other base angle of the isosceles triangle has the same measure, 75°. __

Then x can be found either from the sum of interior angles of the triangle, or from the relation of 105° to the "remote interior angles". The first relation gives ...

75° +75° +x° = 180°   ⇒   x = 180 -150 = 30

The second relation gives ...

  75° +x° = 105°   ⇒   x = 105 -75 = 30

__

y° is supplementary to the left-side base angle, so is ...

  y = 180 -75 = 105

Of course, you could also figure y from the symmetry of the figure.

The values of x, y, z are 30, 105, 75, respectively.