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Giabear23
03.03.2020 •
Mathematics
In the diagram, the measure of angle 5 is (10x -9), and the measure of angle 7 is (9x)". What is the measure of angle 6, to
the nearest degree?
What is the measure of angle 6, to the nearest degree?
81 degrees
90 degrees
99 degrees
105 degrees
Solved
Show answers
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Ответ:
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,
Thus, the value of x is 9.
Substituting
in ∠5 and ∠7, we have,
The measure of
and ![\angle 7= 81^{\circ}](/tpl/images/0532/4459/29c6a.png)
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,
Thus, the measure of angle 6 is 99°
Therefore, Option C is the correct answer.
Ответ:
l = w + 9
area = length * width
52 = l * w
52 = (w+9) w
52 = w^2 + 9w
w^2 + 9w - 52 = 0
w^2 + 13w - 4w - 52 = 0
w (w + 13) - 4 (w + 13) = 0
(w + 13) (w - 4) = 0
length = 13 in
width = 4 in