Triangle Def Contains Two Congruent Acute Angles. The Sum Of The Measures Of The Two Congruent Acute Angles Is Greater Than 90 Degrees. Anna Concludes That The Triangle Must Be An Acute Triangle. Which Best Describes Her Conclusion? She Is Correct. A Tria (2023)

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Triangle Def Contains Two Congruent Acute Angles. The Sum Of The Measures Of The Two Congruent Acute Angles Is Greater Than 90 Degrees. Anna Concludes That The Triangle Must Be An Acute Triangle. Which Best Describes Her Conclusion? She Is Correct. A Tria? ›

Answer and Explanation:

If the sum of two acute angles of a triangle is greater than 90, then the triangle is acute. SOLUTION: True; sample answer: Since the sum of the two acute angles is greater than 90, the measure of the third angle is a number greater than 90 subtracted from 180, which must be less than 90.

In any triangle, we know that the sum of all the angles inside the triangle is 180 degrees. Thus the two acute angles in the right angle triangle will have a sum of 90 degrees.

A right triangle will have two acute angles that add up to 90° because the three angles of any triangle always add up to 180°. A right angle equals 90°, so the remaining two angles of a right triangle are complementary, meaning their sum is 90°.

In a right-angled triangle, the sum of two acute angles is 90∘.

All the three interior angles of an acute triangle measures less than 90°. The angles of an acute triangle add up to 180°.

An acute triangle (or acute-angled triangle) is a triangle with three acute angles (less than 90°). An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles.

A triangle with a right angle and two acute angles is called right angled triangle.

An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent. Thus, in an isosceles right triangle, two legs and the two acute angles are congruent.

Right angle triangle: When the angle between a pair of sides is equal to 90 degrees it is called a right-angle triangle.

Is an acute angle more than 90 or less than 90? ›

Acute angles measure less than 90 degrees. Right angles measure 90 degrees. Obtuse angles measure more than 90 degrees.

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°.

A triangle can have two acute angles because sum of two acute angles will always be less than 180∘ because individually, either angle is less than 90∘.

Hence, the sum of angles of an acute triangle is 180°.

The three interior angles of an acute angle triangle sum up to 180°.

Hence, the sum of any two angles of a triangle is not always greater than the third angle.

A triangle with two right angles is not possible, as the total sum of all the three angles of a triangle is 180∘. If two angles are 90∘, their sum is already 180∘. So, the third angle will be 0∘ which is not possible.

The given statement,”Sum of any two angles of a triangle is always greater than the third angle” is false.

It is a right angle triangle.