Question

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Answer 1

• m∠IMN = 70°

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Set up equations for the vertical angles:

• x + y = 102
• 3x - 26 = y

Rewrite the second equation:

• 3x - y = 26

Add up this with the first equation:

• x + y + 3x - y = 102 + 26
• 4x = 128
• x = 128/4
• x = 32

Find y:

• y + 32 = 102
• y = 102 - 32
• y = 70

The angle IMN is same as y, so its measure is 70°.

Answer 2

∠ IMN = 70°

Explanation:

∠ KIM = ∠ JIL ( vertically opposite angles ), that is

x + y = 102 → (1)

∠ IMN = 3x - 26 ( vertically opposite angles ) , that is

y = 3x - 26 ← substitute into (1)

x + 3x - 26 = 102

4x - 26 = 102 ( add 26 to both sides )

4x = 128 ( divide both sides by 4 )

x = 32

Then

∠ IMN = y = 3x - 26 = 3(32) - 26 = 96 - 26 = 70°