Question

I need help with number 5 number 6 and number 7

Answer 1

Question 5

Two angles are called complementary if their measures add to 90 degrees.

Given:

`\begin{gathered} \angle\text{ 1 is a complement of }\angle2 \\ m\angle2=36^0 \end{gathered}`

Applying the definition for complementary angles, we can write:

`\begin{gathered} m\angle1\text{ + m}\angle2=90^0 \\ m\angle1+36^0=90^0 \\ m\angle1=90^0-36^0 \\ m\angle1=54^0 \end{gathered}`

Answer: 54 degrees

Question 6

Given:

`\begin{gathered} \angle3\text{ is a complement of }\angle4 \\ m\angle4=75^0 \end{gathered}`

Applying the definition for complementary angles, we can write:

`\begin{gathered} m\angle3\text{ + m}\angle4=90^0 \\ m\angle3+75^0=90^0 \\ m\angle3=90^0-75^0 \\ m\angle3=15^0 \end{gathered}`

Answer: 15 degrees

Question 7

Two angles are called supplementary if their measures add to 180 degrees.

Given:

`\begin{gathered} m\angle WXY=(6x+59)^0 \\ m\angle YXZ=(3x-14)^0 \end{gathered}`

Using the definition for supplementary angles, we can write:

`\begin{gathered} m\angle WXY\text{ + m}\angle YXZ=180^0 \\ (6x+59)^0+(3x-14)^0=180^0 \\ \text{collect like terms} \\ 6x\text{ + 3x + 59 -14 = 180} \\ 9x\text{ + 45 = 180} \\ 9x\text{ = 180 - 45} \\ 9x\text{ = 135} \\ \text{Divide both sides by 9} \\ (9x)/(9)\text{ =}(135)/(9) \\ x\text{ = 15} \end{gathered}`

Substituting the value of x into angles WXY and YXZ:

`\begin{gathered} m\angle WXY=(6x+59)^0 \\ =\text{ 6}*15\text{ + 59} \\ =149^0 \\ \\ m\angle YXZ=(3x-14)^0 \\ =\text{ 3}*15\text{ - 14} \\ =31^0 \end{gathered}`

Answer:

The measure of angle WXY = 149 degrees

The measure of angle YXZ = 31 degrees