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

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

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.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this