Answered

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" Theorem: A triangle has at most one obtuse angle. Francisco is proving the theorem above by contradiction. He began by assuming that in ∆ABC, ∠A and ∠B are both obtuse. Which theorem will Francisco use to reach a contradiction?
a. If two angles of a triangle are congruent, the sides opposite the angles are congruent.
b. If two supplementary angles are congruent, each angle measures 90°.
c. The largest angle in a triangle is opposite the longest side.
d. The sum of the measures of the angles of a triangle is 180°. 3"

Sagot :

Reaching a contradiction, Francisco has to state the consequence that contradicts what he has assumed, or state the statement of what he has already known to be true, or both.

When he began assuming that the two angles of the of ΔABC  are both obtuse, he would have to prove by assuming measure of each of the two obtuse angles. The least measurement of an obtuse angle is 91 degrees.  When he adds up the sum of the two angles at 91 degrees each, the sum is 182.

From this, he has reached the contradiction with this consequence: 
Theorem on the sum of the measures of the angles of a triangle which is 180 degrees.  

Because in his assumption, the total of the two obtuse angles is greater than 180 degrees.

The answer is d.
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