Answer:
C:99
Step-by-step explanation:
t 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,
\angle 5 = \angle 7∠5=∠7
10x-9=9x10x−9=9x
10x-9x-9=010x−9x−9=0
x-9=0x−9=0
\begin{lgathered}x=9\\\end{lgathered}
x=9
Thus, the value of x is 9.
Substituting \begin{lgathered}x=9\\\end{lgathered}
x=9
in ∠5 and ∠7, we have,
\angle 5= (10x-9)^{\circ}∠5=(10x−9)
∘
= (10(9)-9)^{\circ}=(10(9)−9)
∘
= (90-9)^{\circ}=(90−9)
∘
= 81^{\circ}=81
∘
\angle 7=(9x)^{\circ}∠7=(9x)
∘
=(9(9))^{\circ}=(9(9))
∘
=81^{\circ}=81
∘
The measure of \angle 5 = 81^{\circ}∠5=81
∘
and \angle 7= 81^{\circ}∠7=81
∘
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,
\angle 6+\angle 7=180^{\circ}∠6+∠7=180
∘
\angle 6+81^{\circ}=180^{\circ}∠6+81
∘
=180
∘
\angle 6=180^{\circ}-81^{\circ}∠6=180
∘
−81
∘
\angle 6 =99^{\circ}∠6=99
∘
Thus, the measure of angle 6 is 99°
Therefore, Option C is the correct answer.