Question

PLEASE PLSASE ANSWER THIS

Answer 1

a = 57.5

b = 57.5

Explanation:

XY=XZ so c=d

`c = d = (180 - 65)/(2) = 57.5`

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

Answer 2

`▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪`

`\fbox \colorbox{black}{ \colorbox{white}{a} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{57.5 \degree}}`

`\fbox \colorbox{black}{ \colorbox{white}{b} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{57.5 \degree}}`

`\large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}`

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°