Question

Hint: The y angle and the (3x - 26) angle are vertical angles. So are the (x+y) and 102 angles. Use those facts to write a two equation system and solve it for x and y. Then you'll be able to find angle IMN

Answer 1

`\angle IMN = 70\°`

Explanation:

Given:

`\angle IMN = y\°\\\\\angle M =(3x-26)\°\\\\\angle JIL =102\°\\\\\angle KIM = (x+y)\°`

We need to find the ∠ IMN

Solution:

Now we know that;

∠ IMN = ∠ M ( Vertically opposite angles)

Substituting the values we get;

`y =3x-26\\\\3x-y =26 \ \ \ \ equation \ 1`

Also We know that;

∠ JIL = ∠ KIM ( Vertically opposite angles)

Substituting the values we get;

`x+y =102 \ \ \ \ equation \ 2`

Now adding equation 1 and equation 2 we get

`(3x-y)+(x+y) =102+26\\\\3x-y+x+y = 128\\\\4x=128`

Dividing both side by 4 using division property of equality we get;

`(4x)/(4) = (128)/(4)\\ \\x= 32`

Now Substituting the value of 'x' in equation 2 we get;

`x+y=102\\\\32+y =102\\\\y =102-32 = 70`

Hence
`\angle IMN = 70\°`