Question

I need help on some geometry questions

Answer 1

Answer: x = 40

Step-by-step explanation:

3x + x + 20 = 180    same side (consecutive) interior angles

    4x  + 20 = 180

    4x           = 160

      x           = 40

****************************************************************************

Answer: x = 24

Step-by-step explanation:

6x - 24 + 2x + 12 = 180       linear pair (supplementary angles)

               8x - 12  = 180

               8x         = 192

                 x          = 24

****************************************************************************

Answer: x = 16

Step-by-step explanation:

base angles of an isosceles triangle are congruent

2(2x + 15) + 6x - 10 = 180       triangle sum theorem

4x + 30 + 6x - 10 = 180

             10x + 20 = 180

              10x         = 160

                 x          = 16

****************************************************************************

Let ∠1 and ∠2 represent the exterior angles in the diagram and "x" represent the same side (consecutive) interior angle with ∠1.

Then m∠1 + x = 180     same side interior angle theorem

and m∠2 + x = 180      linear pairs are supplementary

m∠1 + x = m∠2 + x     transitive property

m∠1  = m∠2               subtraction property of equality

   ∠1 ≈ ∠2                   definition of congruency