The angles are ∠M=116°, ∠O = 64°, ∠N=111° and ∠P=69°.
What is trapezoids?
"Trapezoids are quadrilaterals that have two parallel sides and two non-parallel sides. It is also called a Trapezium. Each pair of opposite angles in an isosceles trapezoid are supplementary, or add up to 180 degrees".
For the given situation,
The angles of trapezium are
∠M = 2 (17y-10)
∠N = 7x-15
∠O = 13y+12
∠P = 3x + 15
The opposite angles are supplementary,
∠M + ∠O = 180° and
∠N + ∠P = 180°.
∠[tex]M[/tex] + ∠[tex]O = 180[/tex]°
⇒[tex]13y+12+2(17y-10)[/tex] [tex]=180[/tex]
⇒[tex]13y+12+34y-20=180[/tex]
⇒[tex]47y = 188\\[/tex]
⇒[tex]y=4[/tex]
On substituting the value of y in ∠M and ∠O, we get
∠[tex]M = 116[/tex]°
∠O = [tex]64[/tex]°
Now consider,
∠[tex]N +[/tex] ∠[tex]P = 180[/tex]
⇒[tex]7x-15+3x+15=180[/tex]
⇒[tex]10x=180[/tex]
⇒[tex]x=18[/tex]
On substituting the value of x in ∠N and ∠P, we get
∠[tex]N=111\\[/tex]°
∠[tex]P=69[/tex]°
Hence we can conclude that the angles are ∠M=116°, ∠O = 64°, ∠N=111°
∠P=69°.
Learn more about trapezoid here
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