Question

/_ RQT is a straight angle. what are m/_RQS and m /_ TQS?

Answer 1

We can find the measure of angles RQS and TQS by applying the theorem below:

The sum of angles on a straight line is 180 degrees

Given:

`\begin{gathered} m\angle RQS=(20x+4)^0 \\ m\angle TQS=(15x+1)^0 \end{gathered}`

Applying the theorem, we have:

`(20x+4)^0+(15x+1)^0=180^0\text{ (angles on a straight line)}`

Simplifying and solving for x:

`\begin{gathered} 20x\text{ + 4 + 15x + 1 =180} \\ \text{Collect like terms} \\ 20x\text{ + 15x + 5 =180} \\ 35x\text{ = 180-5} \\ 35x\text{ = 175} \\ Divide\text{ both sides by 35} \\ (35x)/(35)\text{ = }(175)/(35) \\ x\text{ = 5} \end{gathered}`

When we substitute the value of x , we can find the required angles.

Hence:

`\begin{gathered} m\angle RQS=(20x+4)^0 \\ =\text{ 20}*5\text{ + 4} \\ =\text{ 100 + 4} \\ =104^0 \end{gathered}`

Answer: measure of angle RQS = 104 degrees

`\begin{gathered} m\angle TQS=(15x+1)^0 \\ =\text{ 15 }*\text{ 5 + 1} \\ =\text{ 75 + 1} \\ =76^0 \end{gathered}`

Answer: measure of angle TQS = 76 degrees