Find the values of x and y in the figure

[tex]Find the values of x and y in the figure [/tex]

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Find the values of x and y in the figure

[tex]Find the values of x and y in the figure [/tex]

[tex]x=79^{\circ}\ and\ y=101^{\circ}[/tex]

Step-by-step explanation:

In the given picture, a parallelogram PQRS is given with angle 101°.

In a parallelogram opposite angles are equal.

Since, y is opposite to 101°.

Therefore y=101°

Also, the sum of the adjacent angles of a parallelogram is 180°

[tex]\\\Rightarrow\ x+101^{\circ}=180^{\circ}\\\Rightarrow\ x=180^{\circ}-101^{\circ}\\\Rightarrow\ x=79^{\circ}[/tex]

x = 65, y = 115

Step-by-step explanation:

x and 2x - 15 are adjacent angles and supplementary, thus

2x - 15 + x = 180

3x - 15 = 180 ( add 15 to both sides )

3x = 195 ( divide both sides by 3 )

x = 65

y and 2x - 15 are congruent ( alternate angles ), thus

y = 2x - 15 = 2(65) - 15 = 130 - 15 = 115

x=55 y=125

Step-by-step explanation:

X= 110/2=55

if BC is 110, BAC=250

so Y=250/2=125

180° = x + (2x -15)

180°=3x-15

3x = 195

x =65°

x + y = 180°

65+ y= 180°

y = 115°

[tex]\frac{5}{y} = \frac{5 + 3 }{y + x}[/tex]

[tex]5(y + x) = y( 5 + 3)[/tex]

[tex]5y + 5x = 8y[/tex]

[tex]5x = 8y - 5y[/tex]

[tex]5x = 3y[/tex]

[tex]\frac{x}{y} = \frac{3}{5}[/tex]

[tex]x = 3[/tex]

[tex]y = 5[/tex]

y=180-50+70

y=60

X=110 divided by 2=55 because x is half of the 110 . Since it’s quadratic inside the circle the opposite sides equals to 180 so 180-110=70 so Y =70

x = 160°

Step-by-step explanation:

Angles in a line add up to 180°

∴ 50° + y + 70° = 180°

y = 180° - (50° + 70°) = 60°

Angles in a quadrilateral add up to 360°

Since angle x is equal to the other unknown angle;

x = (360° - 40°) ÷ 2 = 160°