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livinqq1
For the bottom question, I believe the measure of arc RB is 150°.

• External point D (vertex outside of the circle) creates two secant segments (DR and DB).
• Using the exterior angle theorem: angleD= (1/2) RB - EC. This becomes 5x-10 = (13x+7-60°)/2.

• Now solve for x
multiply both sides by 2
10x-20=13x+7-60°
Add/subtract like terms to isolate variable on one side
60° = 3x+27
Subtract 27 from both sides
33=3x
divide both sides by 3 to get variable x alone, and: 11 = x.

• x = 11.

• Plug this x value back into the expression representing arc RB
13(11)+7 = 150.

• mRB=150°.


• check: 5(11)-10=45°. Plug all known values into the exterior angle theorem to see if true; 45° = (1/2)*(150° - 60°)
45°=45°
[true]
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semsee45

Answer:

150°

Step-by-step explanation:

A secant is a straight line that intersects a circle at two points.

The circle shows two secants RD and BD that intersect at one exterior point D, so we can use the Intersecting Secants Theorem to solve.

Intersecting Secants Theorem

If two secant segments are drawn to the circle from one exterior point, the measure of the angle formed by the two lines is half of the (positive) difference of the measures of the intercepted arcs.

[tex]\implies \angle RDB = \dfrac{1}{2}\left(\overset{\frown}{RB}-\overset{\frown}{EC}\right)[/tex]

[tex]\implies 5x-10=\dfrac{1}{2}(13x+7-60^{\circ})[/tex]

[tex]\implies 2(5x-10)=13x-53[/tex]

[tex]\implies 10x-20=13x-53[/tex]

[tex]\implies -3x=-33[/tex]

[tex]\implies x=11[/tex]

To find the measure of [tex]\overset{\frown}{RB}[/tex], substitute the found value of x into the expression for the arc:

[tex]\implies \overset{\frown}{RB}=13x+7[/tex]

[tex]\implies \overset{\frown}{RB}=13(11)+7[/tex]

[tex]\implies \overset{\frown}{RB}=143+7[/tex]

[tex]\implies \overset{\frown}{RB}=150^{\circ}[/tex]

Therefore, the measure of arc RB is 150°.

Learn more about intersecting secants here:

https://brainly.com/question/27934565

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