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10 votes
Find x

S
T
43
(9x -14)
U

Find x S T 43 (9x -14) U-example-1
User Rkrishnan
by
4.7k points

1 Answer

5 votes

Answer:

x = 12°

Welcome to concept of Inscribed Angle theorem

In the diagram shown above, the inscribed angle m∠SUT intercepts the diameter ST.

Then,

m∠SUT = 90°

In Δ SUT,

m∠S + m∠U + m∠T = 180°

Substitute.

m∠S + 90° + 43° = 180°

m∠S + 133° = 180°

Subtract 133° from each side.

m∠S = 47°

m∠UST = 47°

By Inscribed Angle Theorem,

m∠arc UT = 2 ⋅ m∠UST

Substitute.

(9x - 14)° = 2 ⋅ 47°

(9x - 14)° = 94°

9x - 14 = 94

Add 14 to each side.

9x = 108

Divide each side by 9

x = 12

Hence, we get as x = 12°

User Shimanski Artem
by
3.8k points