Question

Can you help and explain what to do with practice question below?

Answer 1

Given the figure below:

To solve for the missing angles,

Step 1: Solve for c.

The sum of the interior angles of a triangle equals 180 degrees.

Thus,

`\begin{gathered} 48+58+c=180(sum\text{ of interior angles in a triangle\rparen} \\ \Rightarrow106+c=180 \\ subtract\text{ 106 from both sides,} \\ 106-106+c=180-106 \\ \Rightarrow c=74\degree \end{gathered}`

Step 2: Solve for d.

The sum of angles on a straight line gives 180 degrees.

`\begin{gathered} 58+d=180\text{ \lparen sum of angles on a straight line\rparen} \\ subtract\text{ 58 from both sides,} \\ 58-58+d=180-58 \\ \Rightarrow d=122\degree \end{gathered}`

Step 3: Solve for a.

From the figure,

`a=58\degree\text{ \lparen alternate angles\rparen}`

Step 4: Solve for b.

From the figure,

`\begin{gathered} b+c=d\text{ \lparen alternate angles\rparen} \\ \Rightarrow b+74=122 \\ subtract\text{ 74 from both sides,} \\ b+74-74=122-74 \\ \Rightarrow b=48\degree \end{gathered}`

Hence, we have

`\begin{gathered} a=58\degree \\ b=48\degree \\ c=74\degree \\ d=122\degree \end{gathered}`