Question

(Problem in attached photo)​

Answer 1

m∠LOM = 48°

Explanation:

Given:

• m∠LON is straight line.
• m∠LOM = 7x - 92°
• m∠LOM = 6x + 12°

To find:

• m∠LOM = ?

Solution:

Since m∠LON is a straight line and they are supplementary, we know that:

m∠LOM + m∠MON = 180°.

Substituting these values, we get:

(7x - 92°) + (6x + 12°) = 180°

Combining like terms, we get:

13x - 80° = 180°

Adding 80° to both sides of the equation, we get:

13x - 80° + 80° = 180° - 80°

13x = 260°

Dividing both sides of the equation by 13, we get:

`\sf (13x)/(13)=(260^\circ)/(13)`

x = 20°

We can find the value of m∠LOM by substituting value of x and simplifying it.

Therefore,

m∠LOM = 7x - 92°

= 7(20°) - 92°

= 140° - 92°

= 48°

So, Answer is:

m∠LOM = 48°

Answer 2

∠ LOM = 48°

Explanation:

∠ LOM and ∠ MON lie on a straight line and form a linear pair , which sum to 180°

sum the 2 angles, equate to 180 and solve for x

7x - 92 + 6x + 12 = 180 ( collect like terms on left side )

13x - 80 = 180 ( add 80 to both sides )

13x = 260 ( divide both sides by 13 )

x = 20

Then

∠ LOM = 7x - 92 = 7(20) - 92 = 140 - 92 = 48°