Question

TV and RI intersect at E. If the measure of IVE=50, the measure of VIE=70 and the measure of RET=2X-10 , find the value of x

Answer 1

The value of x from the given conditions is 35.

The  line TV and RI intersect at E.

The measure of IVE=50° and the measure of VIE=70°.

Since, the points V, I and E makes a triangle.

Therefore, the total angle inside the triangle is 180°.

Hence,

∠IVE + ∠VIE + ∠VEI = 180°

50°+70°+ ∠VEI = 180°

∠VEI = 180°-50°-70°

∠VEI = 60°

Also the angles ∠VEI and the angle ∠RET are congruent.

Therefore, ∠VEI = ∠RET

60° = 2x-10

2x = 70

x = 70/2

x = 35.

The lines TV and RI intersect at E. If the measure of IVE=50, the measure of VIE=70 and the measure of RET=2X-10. Then the value of x = 35.

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Answer 2

Answer:

  x = 35

Step-by-step explanation:

The angle sum theorem can be used to find the congruent vertical angles RET and IEV. The equation relating these can be solved for x.

Missing angle

The missing angle in triangle IVE is found using the angle sum theorem:

  ∠IVE +∠VIE +∠IEV = 180°

  ∠IEV = 180° -50° -70° = 60°

Vertical angle

Vertical angles RET and IEV are congruent:

  ∠RET = ∠IEV

  2x -10 = 60

  2x = 70 . . . . . . . . add 10

  x = 35 . . . . . . . . divide by 2