To solve for the unknown angle "?" in the given triangle diagram, let’s analyze the geometry step by step:

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1. Observing the Triangle:

The diagram shows two sub-triangles. The unknown angle "?" is located at the apex of the larger triangle.

Key given angles:

• Bottom-left: $45^\circ$ and $25^\circ$
• Bottom-right: $50^\circ$ and $20^\circ$

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2. Properties Used:

• The sum of angles in a triangle equals $180^\circ$.
• Adjacent angles on a straight line sum to $180^\circ$.

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3. Solving Step by Step:

Step 1: Bottom-left triangle

In the left triangle:

• Angles are $45^\circ$, $25^\circ$, and an unknown angle at the apex.
• Let this unknown angle at the apex of the left triangle be $x$.

Using the angle sum property: $x + 45^\circ + 25^\circ = 180^\circ$ $x = 180^\circ - 70^\circ = 110^\circ$

Step 2: Bottom-right triangle

In the right triangle:

• Angles are $50^\circ$, $20^\circ$, and an unknown angle at the apex.
• Let this unknown angle at the apex of the right triangle be $y$.

Using the angle sum property: $y + 50^\circ + 20^\circ = 180^\circ$ $y = 180^\circ - 70^\circ = 110^\circ$

Step 3: Solving for the unknown angle

The unknown angle "?" at the apex is formed by the angles $x$ and $y$, which are supplementary angles (together they form a straight line).

$x + y + ? = 360^\circ \quad \text{(full circle around the apex of the larger triangle)}.$ Substituting $x = 110^\circ$ and $y = 110^\circ$: $110^\circ + 110^\circ + ? = 360^\circ$ $? = 360^\circ - 220^\circ = 140^\circ$

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Final Answer:

The unknown angle $?$ is: $\boxed{140^\circ}$

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Would you like further clarification or additional details?

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Related Questions:

1. How can the angle sum property of triangles be applied in irregular shapes?
2. What are supplementary and complementary angles, and how do they differ?
3. How can you calculate angles in polygons with more than three sides?
4. What are some real-world applications of angle calculations in geometry?
5. Can this problem be solved using trigonometry? If so, how?

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Tip:

Always double-check your calculations and label diagrams clearly to avoid confusion in multi-step problems!