Question

PLEASE HELP ASAP
see pic below
PLEASE HELP ASAP!!!!!

Answer 1

Here's a better answer for 5.

See the diagram below.

Follow this argument.

The givens are Circle O with the center at O. Two Tangents coming from A and going to B and C. If you draw lines from O (the center) to B ( a radius) and from A to C (also a radius) you form 2 right angles. The right angles are labeled OBA and OCA

OBAC is a kite. It has three known angles. 2 angles are 90o and the third one is 47 degrees. Every kite is made of 360 degrees. The unknown angle is BOC.

BOC + 90 +90 + 47 = 360

BOC + 227 = 360

BOC = 360 - 227

BOC = 133

That is also a central angle of a circle. The arc opposite the central angle = the central angle

The arc is 133. Answer D

Answer 2

The person is standing 16m from the circular monument park. Her lines of sight form tangent to the monument with an angle of $47^\circ$. Let the arc formed by her sight be the minor arc and the remaining arc of the circular monument be major arc.

Let the measure of minor arc be $x^{\circ}$.

Therefore, the major arc is $360-x^{\circ}$

Now, Applying Tangent-Tangent Angle theorem which states that If an angle is formed by two intersecting tangents, then the measure of the angle is one half the difference of the measures of the intercepted arcs (the major arc minus the minor arc).

So, $\frac{(360^{\circ}-x)-x}{2}=47^{\circ}$

$\frac{(360^{\circ}-2x)}{2}=47^{\circ}$

${(360^{\circ}-2x)}=47^{\circ} \times 2$

${(360^{\circ}-2x)}=94^{\circ}$

$360^{\circ}-94^{\circ}=2x$

$266^{\circ}=2x$

$x=133^{\circ}$