Question

Find measure of angle M

Answer 1

5x+18+4x-9=360

9x+9=360

9x=360-9

9x=351

x=351/9

x=39

therefore, <M=4(39)-9

<M=156-9

<M=147°

Answer 2

☃
`\large{ \tt{STEP - BY -STEP \: EXPLANATION}} :`

☼ Some Questions and their answers which should be known before you start to solve the given question :

☄Do you know what the figure is ?

⇢ The given figure , MNOL is a parallelogram.

☄ Do you know about co-interior angles ?

⇢A pair of interior angles which lies to the same side of transversal is known as co-interior angles. On parallel lines , co - interior [ C ] angles adds up to 180°.

⇾ Our Q/A part ends up here! Now let's start solving :

♨
`\large{ \tt{G \: I\: V \: E \: N}}:`

• MNOL is a parallelogram ,
  `\angle` L = ( 5x + 18 ) °&
  `\angle` M = ( 4x - 9 ) °

☥
`\large{ \tt{T\: O \: \: F \: I \: N \: D}} :`

• measure of
  `\angle` M

☪
`\large{ \tt{S \: O \: L \: U \: T \: I \: O\: N}} :`

• Since MNOL is a parallelogram , MN
  `\parallel` OL.

~Set up an equation & solve for x

۵
`\large{ \tt{(5x + 18) \degree + (4x - 9) \degree = 180 \degree}}` [ Sum of co-interior angles ]

⟿
`\large \tt \: 5x \degree + 18 \degree + 4x \degree - 9 \degree = 180 \degree`

⟿
`\large \tt \: 9x \degree + 9 \degree = 180 \degree`

⟿
`\large \tt \:9x \degree = 180 \degree - 9 \degree`

⟿
`\large \tt \: 9x \degree = 171 \degree`

⟿
`\large \tt \: x \degree = (171 \degree)/(9 \degree)`

⟿
`\large{ \tt{x \: = 19 \degree}}`

• The value of x is 19°. Again , Finding the value of
  `\angle` M :

♕
`\large \tt \: REPLACING \: VALUE:`

• 
  `{ \tt{ \angle \: m = (4x - 9) \degree = (4 * 19 \degree - 9) \degree} = \boxed{ \tt{67 \degree}}}`

☥
`\boxed{ \boxed{ \tt{Our \: Final \: Answer : \boxed{ \underline{ \tt{67 \degree}}}}}}`

✺ If you are studying at 3 :00 am , make sure you are STUDYING because you are sacrificing your sleep! ✔

♡ Hope I helped! ✎

Have a wonderful day / night !

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