Inscribed angles math lib
Need help with 9 and 10 thank you!!

A cyclic quadrilateral is a quadrilateral that is drawn inside a circle. The sum of the opposite angle of the cyclic quadrilateral is always equal to 180°.

9.) As we know that the sum of the opposite angles of a cyclic quadrilateral is supplementary, therefore, their sum is 180°. Thus, we can write for

[tex]\angle GDE + \angle EFG = 180^o\\\\19x - 26 + 7x - 2 = 180\\\\26x - 28 = 180\\\\26x = 208\\\\x = 8[/tex]

Now, substitute the value of x, in order to get the measure of the ∠EFG,

[tex]\angle EFG = 7x - 2\\\\\angle EFG = 7(8) - 2\\\\\angle EFG = 56 - 2\\\\\angle EFG = 54^o[/tex]

The measure of the ∠EFG is 54°.

10.) As we know that the sum of the opposite angles of a cyclic quadrilateral is supplementary, therefore, their sum is 180°. Thus, we can write for

[tex]\angle YXW + \angle YVW = 180^o\\\\21x - 33 + 14x + 3 = 180\\\\35x - 30 = 180\\\\35x = 210\\\\x = 6[/tex]

Now, substitute the value of x, in order to get the measure of the ∠YVW,

[tex]\angle YVW = 14x + 3\\\\\angle YVW = 14(6) + 3 \\\\\angle YVW= 84 + 3 \\\\\angle YVW = 87^o[/tex]

As we know that in the inscribed∠YVW, the ∠YVW is half the measure of its intercepted arc YW, therefore, We can write it as,

arc YW = 2 × 87° = 174°, and

arc XW = 174° - 64° = 110°

The measure of the angle made by the arc XW is 110°.

Learn more about Cyclic Quadrilateral:

https://brainly.com/question/9992339

Inscribed angles math lib Need help with 9 and 10 thank you!!

Respuesta :

What is a Cyclic quadrilateral?

Otras preguntas

Inscribed angles math lib
Need help with 9 and 10 thank you!!