Question

A triangle has angles 80, `(7x -1)` and `(6x -3)` degrees. What is the value of `x`?

Answer 1

`x=8`

Explanation:

`• " the sum of the 3 angles in a triangle "=180^@`

`"thus the 3 given angles sum to 180"`

`rArr80+7x-1+6x-3=180`

`rArr13x+76=180`

`"subtract 76 from both sides"`

`13xcancel(+76)cancel(-76)=180-76`

`rArr13x=104`

`"divide both sides by 13"`

`(cancel(13) x)/cancel(13)=104/13`

`rArrx=8`

`rArr7x-1=(7xx8)-1=55`

`rArr6x-3=(6xx8)-3=45`

`"the angles are "80^@,55^@" and "45^@`

`color(blue)"As a check"`

`80+55+45=180`

Answer 2

`x = 8`

Explanation:

Angle sum property of the `DeltaABC` (say),

`/_A +/_B + /_C = 180^@`

`:. 80 + 7x - 1+ 6x - 3 = 180`

`13x + 76 = 180`

`13x = 104`

`x = 104/13`

`x = 8`

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