awsomesaucek2020
Answered

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Sagot :

absor201

Answer:

∴ m∠KIJ = 18°  and   m∠HIJ = 50°

Thus, option a is correct.

Step-by-step explanation:

From the figure, it is clear that:

m∠KIH = m∠HIJ + m∠KIJ

Given

  • m∠KIH = 68°
  • m∠KIJ = (2x + 6)°
  • m∠HIJ = (9x - 4)°

now substituting m∠KIH = 68°, m∠KIJ = (2x + 6)° and m∠HIJ = (9x - 4)° in the equation

m∠KIH = m∠HIJ + m∠KIJ

68° = (2x + 6)° + (9x - 4)°

switch sides

[tex]\left(2x+6\right)+\left(9x-4\right)=68[/tex]

Group like terms

[tex]2x+9x+6-4=68[/tex]

[tex]11x+2=68[/tex]

Subtract 2 from both sides

[tex]11x+2-2=68-2[/tex]

Simplify

[tex]11x=66[/tex]

Divide both sides by 11

[tex]\frac{11x}{11}=\frac{66}{11}[/tex]

Simplify

[tex]x=6[/tex]

Hence, the value of x = 6

Therefore,

m∠KIJ = (2x + 6)° = 2(6) + 6 = 12 + 6 = 18°

m∠HIJ = (9x - 4)° = 9(6) - 4 = 54 - 4 = 50°

∴ m∠KIJ = 18°  and   m∠HIJ = 50°

Thus, option a is correct.

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