In the diagram below secants PT & PU have been drawn from exterior point P such that the four arcs intercepted have the following ratio of measurements arc RS: arc ST:arc TI: arc UR= 1:4:4:3.

(a) If arc RE= X then write an equation that could be used to solve for x and find the value of x

(b) state the measure of each of the four arcs. RS, ST, TU, and UR

(c) find the measure of angle P

(a) x = 30°

(b) mRS =  30°

mST =  120°

mTU  = 120°

mUR = 90°

Step-by-step explanation:

In the picture attached, the diagram is shown.

(a) Given that m arc RS = x, from the ratios:

m arc ST = 4x

m arc TU = 4x

m arc UR = 3x

The addition of the four arcs must be equal to 360°, then:

x + 4x + 4x + 3x = 360°

12x = 360°

x = 360°/12 = 30°

(b) m arc RS = x = 30°

m arc ST = 4x = 4*30° = 120°

m arc TU = 4x = 4*30° = 120°

m arc UR = 3x = 3*30° = 90°

mRS =  30°

, mST =  120°

,  mTU  = 120°

, mUR = 90°

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b

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step-by-step explanation: