Question

Find the value of x, y, and m

Answer 1

x = 9, y = 41

Explanation:

`\because m\angle ABC = 90\degree \\</p><p>\therefore m\angle ABD+m\angle DBC = 90\degree \\</p><p>\therefore (3x+7)\degree + (5x+11)\degree = 90\degree \\</p><p>\therefore (8x + 18)\degree = 90\degree \\</p><p>8x + 18 = 90\\</p><p>8x = 90-18\\</p><p>8x = 72\\</p><p>x = (72)/(8)\\</p><p>\huge \red {\boxed {x = 9}} \\\\</p><p></p><p>m\angle DBC + m\angle FBC = 180\degree \\(straight \: line \: \angle 's) \\</p><p>(5x + 11)\degree + (3y+1)\degree = 180\degree \\</p><p>(5* 9+11)\degree + (3y+1)\degree = 180\degree \\</p><p>(45+11)\degree + (3y+1)\degree = 180\degree \\</p><p>56\degree + (3y+1)\degree = 180\degree \\</p><p>(3y+1)\degree = 180\degree - 56\degree \\</p><p>(3y+1)\degree = 124\degree \\</p><p>3y + 1 = 124\\</p><p>3y = 123\\</p><p>y = \frac {123}{3}\\</p><p>\huge \purple {\boxed {y = 41}} </p><p>`