Question

In parallelogram CNWK, ZC and ZK are consecutive interior angles. The

measure of ZC is (4a + 7)º and mZK = (7a – 3)º. What is mZC in
degrees?

Answer 1

`J. \:\:71\degree`

Explanation:

CNWK is a
`||^(gm)`

`\therefore m\angle C + m\angle K = 180\degree`

(Adjacent angles of a parallelogram)

`\therefore (4a+7)\degree + (7a-3)\degree = 180\degree\\\\</p><p>\therefore (4a+7+7a - 3)\degree = 180\degree\\\\</p><p></p><p>\therefore (11a+4)\degree = 180\degree\\\\</p><p>\therefore 11a+4 = 180\\\\</p><p>\therefore 11a= 180-4\\\\</p><p>\therefore a= (176)/(11)\\\\</p><p>\therefore a= 16\\\\</p><p>\because m\angle C = (4a+7)\degree\\\\</p><p>\therefore m\angle C = (4* 16+7)\degree\\\\</p><p>\therefore m\angle C = (64+7)\degree\\\\</p><p>\huge \orange {\boxed {\therefore m\angle C = 71\degree}} \\\\</p><p>`