Question

If m<2 = (2x)° and m<5 = (x+6)°, find the value

of ‘x’ and the m<4.

Answer 1

x = 58

`m\angle 4 = 116\degree`

Explanation:

`m\angle 2 = m\angle 6..... (1)\\(alternate \: \angle s) \\\\</p><p>m\angle 5 + m\angle 6 = 180\degree \\(linear \: pair\: \angle s) \\\\</p><p>\therefore m\angle 6 = 180\degree-m\angle 5..... (2)\\\\`

From equations (1) & (2)

`m\angle 2 =180\degree-m\angle 5\\\\</p><p>\therefore (2x)\degree =180\degree-(x+6)\degree \\\\</p><p>\therefore (2x)\degree +(x+6)\degree =180\degree\\\\</p><p>\therefore (2x+x+6) \degree =180\degree\\\\</p><p>\therefore (3x+6) \degree =180\degree\\\\</p><p>3x + 6 = 180\\\\</p><p>3x = 180-6\\\\</p><p>3x = 174\\\\</p><p>x = (174)/(3) \\\\</p><p>\huge \purple {\boxed {x = 58}} \\\\</p><p>\because m\angle 4 = m\angle 2\\(corresponding \: \angle s) \\\\</p><p>\therefore m\angle 4 = (2x)\degree \\\\</p><p>\therefore m\angle 4 = (2* 58)\degree \\\\</p><p>\huge \orange {\boxed {\therefore m\angle 4 = 116\degree}}`