Option C: 99° is the measure of angle 6
Explanation:
It is given that the measure of ∠5 is (10x-9)°
The measure of ∠7 is (9x)°
We need to determine the measure of ∠6
Since, from the diagram it is obvious that the angles 5 and 7 are vertical angles.
And, we know that the vertical angles are always equal.
Thus, we have,
[tex]\angle 5 = \angle 7[/tex]
[tex]10x-9=9x[/tex]
[tex]10x-9x-9=0[/tex]
[tex]x-9=0[/tex]
[tex]x=9\\[/tex]
Thus, the value of x is 9.
Substituting [tex]x=9\\[/tex] in ∠5 and ∠7, we have,
[tex]\angle 5= (10x-9)^{\circ}[/tex]
[tex]= (10(9)-9)^{\circ}[/tex]
[tex]= (90-9)^{\circ}[/tex]
[tex]= 81^{\circ}[/tex]
[tex]\angle 7=(9x)^{\circ}[/tex]
[tex]=(9(9))^{\circ}[/tex]
[tex]=81^{\circ}[/tex]
The measure of [tex]\angle 5 = 81^{\circ}[/tex] and [tex]\angle 7= 81^{\circ}[/tex]
Since, from the diagram we can see that the angles 6 and 7 are in a straight line.
And the angles in the straight line add up to 180°
Thus, we have,
[tex]\angle 6+\angle 7=180^{\circ}[/tex]
[tex]\angle 6+81^{\circ}=180^{\circ}[/tex]
[tex]\angle 6=180^{\circ}-81^{\circ}[/tex]
[tex]\angle 6 =99^{\circ}[/tex]
Thus, the measure of angle 6 is 99°
Therefore, Option C is the correct answer.
