Question

Use the image to find angles Q and U. Explain your reasoning.Time ElaAttempt du1 Hour, 75UTGiven :• line UTS || line PQR• m23 = 450• mZ1 = 50°• m26 = 1350s2 314EditView InsertFormatToolsTableBU

Answer 1

We will start by first finding angle U and the proceed to find Q.

Angle U:

Consider this part of the figure given:

Since a transversal cuts the two parallel lines and the interior corresponding angles made by the transversal with the parallel lines are U and < 1, we can apply the theorem that states:

"The sum of corresponding interior angles is 180 degrees"

This is done below:

`\begin{gathered} U+\angle1=180^0\text{ (Sum of corresponding interior angles is 180)} \\ \text{ Since <1 = 50} \\ U+50^0=180^0 \\ \text{subtract 50 from both sides} \\ U=180-50 \\ \therefore U=130^0 \end{gathered}`

Now that we have U, let us find <2.

Angle <2:

For this, we need to consider some steps.

First of all, we need to find "The sum of angles on a line is 180 degrees"

Inspecting the sketch from the figure above, we can apply the above theorem:

`\begin{gathered} \angle6+\angle\text{QST}=180^0\text{ (sum of angles on a straight line)} \\ \angle6=135^0\text{ (From the question)} \\ 135+\angle\text{QST}=180^0 \\ \text{subtract 135 from both sides} \\ \angle\text{QST}=180-135 \\ \therefore\angle\text{QST}=45^0 \end{gathered}`

Now that we know QST, we can use QST to find

Since we know <3 = 45, we can use the theorem that states that "The sum of interior angles of a triangle is equal to the opposite exterior angle" to get

`\begin{gathered} \angle\text{QST}+\angle3=\angle\text{QTU} \\ 45+45+\angle\text{QTU} \\ \\ \therefore\angle\text{QTU}=90 \end{gathered}`

We can also apply the same theorem to find angle 2

Therefore, the final answers are:

< U = 130

< 2 = 40