Question

Solve the problem below

Answer 1

Answer:  207 degrees

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Explanation:

Refer to the diagram below.

There's a lot of info given to us that we don't need (and won't use).

The only key piece of info we'll really use is the fact that angle XZY is 27 degrees.

Draw in segments RU and RT to form quadrilateral TRUZ

Focusing solely on this quadrilateral, we see that the angles T and U are 90 degrees each (since the tangents are perpendicular to the radii at the point of tangency). Furthermore, we see that angle Z is 27 while angle R is x

For any quadrilateral, the four angles always add to 360 degrees

T+R+U+Z = 360

90+x+90+27 = 360

x+207 = 360

x = 360-207

x = 153

That means angle R of quadrilateral TRUZ is 153 degrees.

Furthermore, it means angle TRU is 153 degrees.

By extension, it indicates that minor arc TU is 153 degrees.

That makes arc TSU = 360 - (minor arc TU) = 360 - 153 = 207 degrees

Answer 2

By Joining TR and UR we got 2 right angles and a Quadrilateral

now

In a Quadrilateral sum of angles=360°

$\\ \large\sf\longmapsto x+90+90+27=360$

$\\ \large\sf\longmapsto x+180+27=360$

$\\ \large\sf\longmapsto x+207=360$

$\\ \large\sf\longmapsto x=360-207$

$\\ \large\sf\longmapsto x=153°$

• <TSU =360-153=207°