Question: Which of the following equations could be used to
find the missing angle measure?
180 − q = 29 + 45
None of these
q + 90 = 29 + 45
29 + 45 = q
Graph: a shaded triangle-like shape on the left has angles labeled 29° at the left vertex, 45° at the bottom-right vertex, and q° at the top vertex with an exterior ray extending upward from that top vertex; position_hint = top-left.
1. **State the problem:** We need to find which equation can be used to find the missing angle $q$ in a triangle with angles $29^\circ$, $45^\circ$, and $q^\circ$.
2. **Recall the triangle angle sum rule:** The sum of the interior angles of a triangle is always $$180^\circ$$.
3. **Set up the equation:** Since the angles are $29^\circ$, $45^\circ$, and $q^\circ$, the sum is:
$$29 + 45 + q = 180$$
4. **Simplify the known angles:**
$$74 + q = 180$$
5. **Isolate $q$:**
$$q = 180 - 74$$
$$q = 106$$
6. **Check the given options:**
- Option 1: $$180 - q = 29 + 45$$ which rearranges to $$180 - q = 74$$, equivalent to $$q = 180 - 74$$, which matches our equation.
- Option 2: "None of these" is incorrect because option 1 works.
- Option 3: $$q + 90 = 29 + 45$$ or $$q + 90 = 74$$, which is incorrect.
- Option 4: $$29 + 45 = q$$ or $$74 = q$$, which is incorrect.
**Final answer:** The correct equation is $$180 - q = 29 + 45$$.