Question

ana tried to prove that an exterior triangle angle measure equals the sum of the measures of the two interior angles not adjacent to it.

triangle diagram with points a, b, c, d and angles 1, 2, 3, 4

statement	reason
2 ( mangle3 + mangle4 = 180^circ )	the angle measures of a linear pair sum to ( 180^circ ).
3 ( mangle1 + mangle2 + mangle3 = mangle3 + mangle4 )	substitution
4 ( mangle1 + mangle2 = mangle4 )	subtract ( mangle3 )

what was the first mistake in anas proof?

choose 1 answer:

a ( mangle1 + mangle2 + mangle3 = 180^circ ) was not given.

b ( angle3 ) and ( angle4 ) arent a linear pair.

c the substitution isnt correct.

d we cant subtract an angle measure from both sides of an equation.

Explanation:

To determine the first mistake in Ana's proof, we analyze each option:

• Option B: ∠3 and ∠4 are a linear pair (they form a straight line at point C), so this is incorrect.
• Option C: The substitution step is correct (since both sides equal 180°, they can be set equal), so this is incorrect.
• Option D: Subtracting an angle measure from both sides of an equation is a valid algebraic operation, so this is incorrect.
• Option A: The sum of the interior angles of a triangle (\(m\angle1 + m\angle2 + m\angle3 = 180^\circ\)) is a theorem (Triangle Angle Sum Theorem), not a "given" in the context of proving the exterior angle theorem. Ana incorrectly labeled this as "Given" when it should be justified by the theorem, making this the first mistake.

Answer:

A. \( m\angle1 + m\angle2 + m\angle3 = 180^\circ \) was not given.