Please help I am not sure how to solve this problem.

Measure of arc TSU = 201°

Step-by-step explanation:

For the inscribed circle of  triangle XYZ, we have;

∠XZY = 21°

Segment TZ and segment  UZ are tangent to circle R

Therefore, ∠ZUR = ∠ZTR = 90° (angle formed by a tangent)

Length UR = Length TR = Radius of circle R

∴ ΔZTR ≅ ΔZUR Side Angle Side (SAS) rule of Congruency

∴ ∠RZT ≅ ∠RZU, (Congruent Parts of Congruent Triangles are Congruent, CPCTC)

∠XZY = ∠RZT + ∠RZU (Angle summation)

21° = ∠RZT + ∠RZU  = 2×∠RZU (Transitive property)

∠RZU = 21°/2 = 10.5° = ∠RZT

∴ ∠URZ = 180- 90 - 10.5 = 79.5° = ∠TRZ (CPCTC)

arc TU = ∠URT = ∠URZ + ∠TRZ = 79.5 + 79.5 = 159° (angle addition)

∴ Measure of arc TSU = 360° - 159° = 201° (Sum of angles at the center of the circle R)

Measure of arc TSU = 201°.

(x-2) ( x+2) ( 2x + 5)

Step-by-step explanation:

We will factor the given expression by grouping

The expression is 2x³ + 5x² - 8x - 20

= ( 2x³ + 5x² ) - ( 8x + 20 )

= x² (2x + 5) - 4(2x + 5)  [ distributive property ]

= (a² -4) ( 2x + 5)

= (x-2) (x+2) (2x+5)  [since a² - b² = ( a+b ) (a-b) ]

Then the factored form of the expression will be (x-2) ( x+2) ( 2x + 5)