Respuesta :

watsonultra2

Answer:

a = 57.5

b = 57.5

Step-by-step explanation:

XY=XZ so c=d

[tex]c = d = \frac{180 - 65}{2} = 57.5[/tex]

Now draw the XH

So angle YXH = 180 — 90 — 57.5 = 32.5

a+YXH=90

a+32.5=90

so a = 57.5

We know that a + 65 + b = 180

So 57.5 + 65 + b = 180

b = 180 — 122.5

b = 57.5

DᴀʀᴋPᴀʀᴀᴅᴏx

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

[tex] \fbox \colorbox{black}{ \colorbox{white}{a} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{57.5 \degree}}[/tex]

[tex]\fbox \colorbox{black}{ \colorbox{white}{b} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{57.5 \degree}}[/tex]

[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]

From the above diagram we can conclude that ~

Angle c = Angle a (Alternate interior Angle pair)

Angle d = Angle b (Alternate interior Angle pair)

and,

  • Angle c = Angle d

because their opposite sides are equal.

now, according to linear pair property ~

  • Angle a + Angle b + 65° = 180°

replacing Angle a with Angle c and Angle d with Angle b, because they are equal to one another ~

  • Angle c + Angle d + 65° = 180°

  • 2 × Angle c = 180° - 65°

(because Angle c = Angle d)

  • 2 × Angle c = 115°

  • Angle c = 115° ÷ 2

  • Angle c = 57.5° = Angle d

So,

  • Angle a = Angle c = 57.5°

  • Angle b = Angle d = 57.5°

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