Question

M∠lonm, angle, l, o, n is a straight angle. \qquad m \angle lom = 9x - 91^\circm∠lom=9x−91 ∘ m, angle, l, o, m, equals, 9, x, minus, 91, degrees \qquad m \angle mon = 6x + 76^\circm∠mon=6x+76 ∘ m, angle, m, o, n, equals, 6, x, plus, 76, degrees find m\angle monm∠monm, angle, m, o, n:

Answer 1

Given:

The angle $\angle LON$ is a straight angle.

$\angle LON = (9x-91)^\circ$

$\angle MON = (6x+76)^\circ$

To find:

$\angle MON = ? ^\circ$

Solution:

As per given statement:

$\angle LON = 180^\circ$ (straight angle)

Please refer to the attached image for clear picture of the given dimensions.

Point M is such that $\angle LON$ is divided into two parts:

$m\angle LOM$ and $m\angle MON$.

$\angle LON$ = $m\angle LOM$ + $m\angle MON$

Putting values

$m\angle LOM$ = $(9x-91)^\circ$

$m\angle MON$ = $(6x+76)^\circ$

$180^\circ = (9x-91)^\circ+(6x+76)^\circ\\\Rightarrow 180 = 15x-15\\\Rightarrow 15x = 195\\\Rightarrow x = 13$

Putting x=13 in $m\angle MON$ = $(6x+76)^\circ$

$m\angle MON$ =

$(6 \times 13 +76)^\circ = (78+76)^\circ\\\Rightarrow 154^\circ.$

The answer is $m\angle MON$ = $154^\circ$

Answer 2

Answer:

154

Step-by-step explanation:

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