Question

HELP!!!!!!

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

Answer 1

(a) x = 30°

(b) mRS = 30°

mST = 120°

mTU = 120°

mUR = 90°

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°