Question

Solve for x and the measurement of ABC

Answer 1

`\\ \ast\sf\hookrightarrow 5x-13+8x+3=180`

`\\ \ast\sf\hookrightarrow 13x-10=180`

`\\ \ast\sf\hookrightarrow 13x=180-10=170`

`\\ \ast\sf\hookrightarrow x=(170)/(13)`

`\\ \ast\sf\hookrightarrow x\approx 13`

Now

`\\ \ast\sf\hookrightarrow m<ABC=5x-13`

`\\ \ast\sf\hookrightarrow 5(13)-13`

`\\ \ast\sf\hookrightarrow 65-13`

`\\ \ast\sf\hookrightarrow 52`

Answer 2

m‹ABC + m‹DBC = 180° [ angles on a straight line ]

`{ \tt{(5x - 18) \degree + (8x + 3) \degree = 180 \degree}} \\ \\ { \tt{13x - 15 = 180}} \\ \\ { \tt{13x = 195}} \\ \\ { \tt{x = 15}}`

m‹ABC = 5(15)-18

m‹ABC = 57°