Question

In the picture below, measure 1 is 5x-14 degrees and measure 3 is 2x+10 degrees. Find measure 2.

Answer 1

Step 1:

In this question, we have the following:

In the picture below, measure 1 is (5x-14) degrees and measure 3 is (2x+10) degrees.

Find the measure of 2.



Step 2:

From the diagram, we can see that angles 1 and 3 are vertically opposite and they are also equal.

Based on this fact, we can see that:

`\begin{gathered} \angle\text{1 = }\angle3 \\ (\text{ 5 x- 14 ) = ( 2x + 10 )} \\ \text{collecting like terms, we have that:} \\ 5x\text{ - 2x = 10 + 14} \\ \text{3 x = 24} \end{gathered}`

Divide both sides, we have that:

`\begin{gathered} x\text{ =}(24)/(3) \\ \text{x = 8 } \end{gathered}`

Then, we put x = 8 into the equation for Angle 1 , we have that:

`\angle1=(5x-14)=5(8)-14=40-14=26^0`
`\angle3=(2x+10)=2(8)+10=16+10=26^0`

Hence, we can see that Angles 1 and 3 are equal.

Step 3:

From the diagram, we can see that:

we can see that angles 2 and 4 are vertically opposite and they are also equal.

Recall that angles 1 and 3 are also vertically opposite and they are also equal.

Therefore, we can see that:

`\begin{gathered} \angle2\text{ = p} \\ \angle4\text{ = p} \\ \angle1\text{ = }26^0 \\ \angle3=26^0 \\ \text{Then, we have that:} \\ p+p+26^0+26^{\text{ 0 }}=360^0\text{ ( Sum of angles at a point)} \\ 2p+52^0=360^0 \\ 2p=360^0-52^0 \end{gathered}`

Divide both sides by 2, we have that:

`\begin{gathered} 2p=308^0 \\ p\text{ =}(308^0)/(2) \\ p=154^0 \end{gathered}`

CONCLUSION: