Question

what is the value of u?

u = \boxed{\circ}

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Explanation:

Step1: Use exterior angle theorem

The exterior angle of a triangle equals the sum of the two opposite interior angles, so:
$u + 46^\circ = (2u - 9^\circ) + (2u - 11^\circ)$

Step2: Simplify right-hand side

Combine like terms:
$u + 46 = 4u - 20$

Step3: Isolate variable terms

Subtract $u$ from both sides:
$46 = 3u - 20$

Step4: Isolate constant terms

Add 20 to both sides:
$66 = 3u$

Step5: Solve for u

Divide both sides by 3:
$u = \frac{66}{3}$

Answer:

$22$