Question

In an obtuse isosceles triangle the angle measurements are, x∘, x∘, and (10x−2)=128∘. Find the measurement of one of the acute angles.

Answer 1

Answer:

26°

Step-by-step explanation:

An obtuse triangle is a triangle that has one obtuse angle. Obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees.

An isosceles triangle is a triangle that has two equal sides and angles.  

Therefore, an obtuse isosceles triangle is a triangle with an obtuse angle and two equal sides that have two equal acute angles (angle less than 90° ).

Given:

The three angles of the triangle are given to be x°, x°  and (10x−2) = 128°. The obtuse angle is 128°, the two x° are acute angles. We are not using equation 10x − 2 since the value of the obtuse angle has been given as 128°

The sum of angles in a triangle is 180°

∴  x° + x° + 128° = 180°

2x° = 180° - 128°

2x° = 52°

x° = 52° / 2

x° = 26°

The measurement of one of the acute angles is 26°