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Sagot :
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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