8. The measures of the exterior angles of a convex quadrilateral are $$ 90^{\circ}, 10 x^{\circ}, 5 x^{\circ} $$, and $$ 45^{\circ} $$ What is the measure of the largest exterior angle?

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1. The sum of the exterior angles of any convex polygon is $$360^\circ$$. Therefore, we have:
   $$
   90 + 10x + 5x + 45 = 360
   $$

2. Combine like terms:
   $$
   10x + 5x = 15x \quad \text{and} \quad 90 + 45 = 135
   $$
   So the equation becomes:
   $$
   15x + 135 = 360
   $$

3. Solve for $$x$$ by subtracting $$135$$ from both sides:
   $$
   15x = 360 - 135 = 225
   $$
   Divide both sides by $$15$$:
   $$
   x = \frac{225}{15} = 15
   $$

4. Substitute $$x = 15$$ back into the measures of the angles:
   - First angle: $$90^\circ$$
   - Second angle: $$10x = 10 \times 15 = 150^\circ$$
   - Third angle: $$5x = 5 \times 15 = 75^\circ$$
   - Fourth angle: $$45^\circ$$

5. The largest exterior angle is therefore:
   $$
   150^\circ
   $$
The largest exterior angle is $$150^\circ$$.

The measures of the exterior angles of a convex quadrilateral are , and
What is the measure of the largest exterior angle?

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The measures of the exterior angles of a convex quadrilateral are , and What is the measure of the largest exterior angle?