☃ [tex] \large{ \tt{STEP - BY -STEP \: EXPLANATION}} : [/tex]
☼ 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 :
♨ [tex] \large{ \tt{G \: I\: V \: E \: N}}:[/tex]
- MNOL is a parallelogram , [tex] \angle[/tex] L = ( 5x + 18 ) °& [tex] \angle[/tex] M = ( 4x - 9 ) °
☥ [tex] \large{ \tt{T\: O \: \: F \: I \: N \: D}} : [/tex]
- measure of [tex] \angle[/tex] M
☪ [tex] \large{ \tt{S \: O \: L \: U \: T \: I \: O\: N}} : [/tex]
- Since MNOL is a parallelogram , MN [tex] \parallel[/tex] OL.
~Set up an equation & solve for x
۵ [tex] \large{ \tt{(5x + 18) \degree + (4x - 9) \degree = 180 \degree}}[/tex] [ Sum of co-interior angles ]
⟿ [tex] \large \tt \: 5x \degree + 18 \degree + 4x \degree - 9 \degree = 180 \degree[/tex]
⟿ [tex] \large \tt \: 9x \degree + 9 \degree = 180 \degree[/tex]
⟿ [tex] \large \tt \:9x \degree = 180 \degree - 9 \degree[/tex]
⟿ [tex] \large \tt \: 9x \degree = 171 \degree[/tex]
⟿ [tex] \large \tt \: x \degree = \frac{171 \degree}{9 \degree} [/tex]
⟿ [tex] \large{ \tt{x \: = 19 \degree}}[/tex]
- The value of x is 19°. Again , Finding the value of [tex] \angle[/tex] M :
♕ [tex] \large \tt \: REPLACING \: VALUE: [/tex]
- [tex] { \tt{ \angle \: m = (4x - 9) \degree = (4 \times 19 \degree - 9) \degree} = \boxed{ \tt{67 \degree}}}[/tex]
☥ [tex] \boxed{ \boxed{ \tt{Our \: Final \: Answer : \boxed{ \underline{ \tt{67 \degree}}}}}}[/tex]
✺ 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 !
# StayInAndExplore ☂
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