The value of angle
and the value of
![\( x \) is \( 7.75 \).](https://img.qammunity.org/2022/formulas/mathematics/high-school/mqkr9unoz1ud0gbfmhdfzvon2n8fq6ygmg.png)
In a kite, adjacent angles are supplementary (they add up to 180 degrees) because a kite has two distinct pairs of adjacent congruent sides.
Given the kite XYZW , with the angles marked as:
![- Angle \( X = (12x - 9)^\circ \)](https://img.qammunity.org/2022/formulas/mathematics/high-school/u220y3x1zp53wo6lb8tza5lzfy3huf63ya.png)
![- Angle \( Y = 96^\circ \)](https://img.qammunity.org/2022/formulas/mathematics/high-school/ucn3xxea6tx6wxgoohlamhzez74g2sczm0.png)
![- Angle \( Z = (17x + 3)^\circ \)](https://img.qammunity.org/2022/formulas/mathematics/high-school/uh97os39khgic41qlzz55wnpc18xykx1yt.png)
Since X and Y are adjacent, they are supplementary. Therefore:
![\[ (12x - 9) + 96 = 180 \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/qs0cv9lkigsn5vfv1i13gv2sku4h6fd8rc.png)
Now, let's solve for x :
![\[ 12x - 9 + 96 = 180 \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/hjt1ggow3e2vd7ipoyzs5q12g2g5ql62me.png)
![\[ 12x + 87 = 180 \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/g49eo5tiijvxwh239xaxi14kqlskalpemd.png)
![\[ 12x = 180 - 87 \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/mu6f2y4jhu23xdb3spygkcq6ef3cuib21h.png)
![\[ 12x = 93 \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/ua8q5cwbcd20qbkkdznjvwm7w9v3wmd6h5.png)
![\[ x = (93)/(12) \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/3to8zfpuzm7580ofodctljpomzyzdysjx3.png)
![\[ x = 7.75 \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/l0p2kh9sm8woxm9x6onwwtrhd007i6adig.png)
So,
Now, we can calculate the angle X using the value of x :
![\[ X = 12(7.75) - 9 \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/304zq3if94mjjiwuu5ftz33xbzx8masb7b.png)
![\[ X = 93 - 9 \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/5yp12mdgokx8es2cri9jr11wd8uysyngdj.png)
![\[ X = 84^\circ \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/9lvakstc9amej05ixzvn0dm68tiohjpbo0.png)