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Naddika [18.5K]
2 years ago
6

Find measure of angle M

Mathematics
2 answers:
Oksana_A [137]2 years ago
6 0

Answer:

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°

WINSTONCH [101]2 years ago
4 0

☃ \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 = \frac{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 \times 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 !

# StayInAndExplore ☂

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