Which event is most likely to occur? a. flipping a fair coin, with sides labeled heads and tails, and the coins landing on tails. b. choosing a marble out of a bag, with face labeled one to six, and the cube landing on a number less than six . c. rolling a fair number cube, with faces labeled one to six, and the cube landing on a number less than six. d. spinning the arrow on a spinner, with four equal sector labels one to four, and the arrow landing on a number greater than one

∠RQT = 23.5

∠PQR  = 133°

Step-by-step explanation:

Step 1 - Add angles together:

As all angles on a straight line must add up to 180°:

3x - 5 + x + 1 = 180

Add like terms together

3x + x - 5 + 1

4x - 4 = 180

Step 2 - Add 4 to both sides of the equation:

4x - 4 + 4 = 180 + 4

4x = 184

Step 3 - Divide both sides by 4:

x = 46

∠RQS = x + 1

∠RQS = 46 + 1

∠RQS = 47

Given the ray QT bisects ∠RQS, the angles must be the same on either side so:

47 ÷ 2 = ∠RQT

∠RQT = 23.5

As we know the value of x:

∠PQR = 3x - 5

Plug known values in:

3x - 5

3(46) - 5

138 - 5

∠PQR  = 133°

This can also be calculated by subtracting known angle ∠RQS from 180:

180 - 47 = 133.

Hope this helps!