MP Board · Class 9 · Mathematics · TrianglesAn exterior angle of a triangle measures $110^\circ$. If one of its interior opposite angles is $45^\circ$, what is the measure of the other interior opposite angle?
Step-by-Step Solution
According to the Exterior Angle Theorem, an exterior angle of a triangle is equal to the sum of its two interior opposite angles. $$\text{Exterior Angle} = \text{Angle } 1 + \text{Angle } 2$$ $$110^\circ = 45^\circ + x$$ $$x = 110^\circ - 45^\circ = 65^\circ$$ \nTherefore, the other interior opposite angle is $65^\circ$.
Detailed Options Breakdown
Option : $45^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.
Option 1: $55^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.
Option 2: $65^\circ$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: $75^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Triangles.
💡 Study Guide: This question tests core syllabus concepts from Triangles. For formulas, key summaries, and mock exam reference guides, read the full Triangles Revision Notes.