Question

Find the measure of the arc or angle indicated. Part 1. NO LINKS.​

Answer 1

9514 1404 393

Answer:

  1) 62°

  3) 99°

  5) 85°

Step-by-step explanation:

The relevant relationships are ...

• an inscribed angle is half the measure of the arc it intercepts
• the total measure of the arcs of a circle is 360°

__

1) Arc QR has twice the measure of inscribed angle QSR, so is ...

  QR = 2×31° = 62°

__

3) Arc YZ is twice the measure of angle X, so is 2×68° = 136°. The sum of arcs around a circle is 360°, so ...

  arc XZ = 360° -125° -136° = 99°

__

5) The sum of arcs around a circle is 360°, so ...

  arc JZY = 360° -120° -70° = 170°

Angle X is half the measure of arc JZY, so is ...

  angle X = 170°/2 = 85°

Answer 2

Answer:

Step-by-step explanation:

1)

O = center of circle (origin)

we know that the angle at the center of the circle ∠ ROS will be

180= 2(31) + ∠x

180-62 = ∠x

118° = ∠x

The supplemental angle to the 118° will be 62°

62° is the interior angle to  arc QR , so

arc QR is also 62°

3)

b/c the intercepted arc YZ = 2* 68=136

then 136+125+? = 360

? = 99°

arc ZX = 99°

5)

O= center point

we are given the two arcs  120 and 70 for both of these we know that the

interior angles will be the same.  ∠JOX  has a central angle of 120 , then

b/c triangle JOX is an isosceles,  we know that the two angles J and X of

the triangle JOX will be 1/2 of  60 , or 30 each

also for    

also ∠XOY has an interior angle of 70 so the two angle at X and Y will be 1/2 of 110 , or 55°

now add 55+30 to find X for box XYZJ

85° = ∠X