Question

Find the angle measure x in the following figures.

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Answer 1

Answer:

Step-by-step explanation:

A) draw an angle 'A' after 70 degrees

   draw another angle 'B' after 60 degrees

   now, angle A =  180 - 70 = 110 degrees (linear pair)

   angle B = 180 - 60 = 120 degrees (linear pair)

  Total internal angle of a 5 sided polygon = 2 - 5 * 180 = 3 * 180 = 540 degrees

  now,

  x + x + 30 + 110+ 120 = 540 degrees

= 2x + 30 + 110 + 120 =  540

=2x = 540 - (30+110+120) = 540 - 260 = 280

= x = 280/2 = 140 degrees

= x = 140 degrees (question A)

B) Total internal angle of a 5 sided polygon = 2-5*180 = 3*180 = 540 degrees

now,

all the angle are x degrees (all sides are same thus angle are also same)

so,

5x = 540

x = 540/5 = 108

x = 108 degrees (question B)

C) draw an angle 'a' which is below the 60 degrees and to the left of 90 degrees (on the external angle at the bottom of the figure)

now,

angle a = 180 - 90 = 90 degrees (linear pair)

now,

total exterior angle of any figure = 360 degrees

so,

x + 90 + 60 + 90 + 70 = 360 degrees

x = 360 - (90 + 60 + 90 + 70) = 360 - 310 = 50

x = 50 degrees (question C)

phew, I hope this helped :)

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