Given the regular hexagon, find the measure of each numbered angle.

m∠1=60°, m∠2=30°, m∠3=60°

Option C is correct.

Step-by-step explanation:

Given a regular hexagon

we have to find the measure of  ∠1, ∠2 and ∠3

As the angle formed at the centre of circle is 360° and the diagonals of hexagon divides the hexagon into 6 congruent triangles implies the angle at the centre of these 6 congruent triangles are equal.

∴

In ΔFOE, by angle sum property

∠FOE+∠OEF+∠3=180°

60°+2∠3=180°      (∵ OF=OE both are radius)

2∠3=120°

∠3=60°

⇒ ΔFOE is equilateral triangle.

Hence, all 6 are equilateral triangles

In ΔOGD, by angle sum property

∠2+∠OGD+∠ODG=180°

∠2+90°+60°=180

∠2=30°

∠1=60°, ∠2=30°, ∠3=60°

Hence, option C is correct.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.