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FInd the angle x for each diagram.

Mar 14, 2021

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Here's a diagram with all the angles labeled with letters so that it is easier to talk about.

9)

m∠E   =   55°   because it is the other base angle of an isosceles triangle.

m∠D   =   180°  -  55°  -  55°   =   70°   because the sum of the interior angles in a triangle is  180°

m∠C   =   m∠D   =   70°     because they are vertical angles and vertical angles are congruent.

m∠B   =   m∠C   =   70°     because they are base angles of an isosceles triangle.

m∠A   =   180° - 70° - 70°   =   40°

And so...back to the main question...

m∠2  =  m∠A   =   40°       And so...

40  =   7x - 2

Solve the above equation for  x  to get the final answer.

10)

m∠I   =   76°     because they are base angles of an isosceles triangle.

m∠H  =   180° - 76° - 76°   =   28°       because the sum of the interior angles in a triangle is  180°

m∠G  =  90° - m∠H   =   90° - 28°   =   62°       because the sum of  ∠G  and  ∠H  is  90°

m∠F   =   m∠G   =   62°       because they are base angles of an isosceles triangle

And so....back to the main question...

m∠2   =   m∠F   =   62°

62   =   x + 74

x   =   -12

Mar 15, 2021