Answer:
Measurement of all angle= [tex]76.79\º+102.66\º+15.35\º+265.16\º= 360\º[/tex]
Step-by-step explanation:
Given angles are [tex]x\º, (\frac{5x}{9} +60)\º, (\frac{x}{5} )\º, (4x-142)\º[/tex]
The given is a quardilateral.
We know the sum of all angles of quardilaterals is 360º
∴ [tex]x\º+ (\frac{5x}{9} +60)\º+ (\frac{x}{5} )\º+(4x-142)\º= 360\º[/tex]
Now, solving the equation to find value of x.
⇒ [tex]x\º+ (\frac{5x}{9} +60)\º+ (\frac{x}{5} )\º+(4x-142)\º= 360\º[/tex]
Opening parenthesis.
⇒ [tex]x\º+ \frac{5x}{9} +60\º+ \frac{x}{5} \º+4x-142\º= 360\º[/tex]
⇒ [tex]5x\º+ \frac{5x}{9} + \frac{x}{5} \º-82\º= 360\º[/tex]
Adding both side by 82
⇒ [tex]5x+ \frac{5x}{9} + \frac{x}{5} = 442[/tex]
Taking LCD 45
⇒ [tex]\frac{45\times 5x+ 5\times 5x+9x}{45} = 442[/tex]
Multiplying both side by 45
⇒ [tex]225x+25x+9x= 19890[/tex]
⇒[tex]259x= 19890[/tex]
Dividing both side by 259
⇒[tex]x= \frac{19890}{259}[/tex]
∴[tex]x= 76.79\º[/tex]
Next subtituting the value of x to find measurement of other interior angle.
[tex]x\º, (\frac{5x}{9} +60)\º, (\frac{x}{5} )\º, (4x-142)\º[/tex]
2. [tex](\frac{5x}{9} +60)\º[/tex]
= [tex]\frac{5\times 76.79}{9} +60= 42.66+ 60[/tex]
= [tex]102.66\º[/tex]
3. [tex](\frac{x}{5} )\º[/tex]
= [tex](\frac{76.79}{5} )\º= 15.35\º[/tex]
4. [tex](4x-142)\º[/tex]
= [tex]4\times 76.79- 42= 307.16-42[/tex]
= [tex]265.16\º[/tex]