Question

The sum of the measures of the angles of all triangles is 180⁰. If one angle of the triangle measures 45⁰, and the other two angles are equal, what is the measure of each of the other two angles?

Answer 1

To find the measure of the two equal angles in a triangle with one angle measuring 45°, set up the equation 45° + x + x = 180° and solve for 'x', which yields each of the other angles to be 67.5°.

Step-by-step explanation:

The question concerns the properties of a triangle and its angles. In this specific problem, one angle of the triangle is given as 45°, and we are told that the other two angles are equal. Knowing that the total sum of angles in any triangle is always 180°, we can identify the measure of the other two angles.

Let's denote the measure of each of these two equal angles as 'x'. Therefore, we can write the equation:

45° + x + x = 180°

To find the value of 'x', we combine the like terms (the two 'x' terms) and then rearrange the equation:

45° + 2x = 180°

Next, we subtract 45° from both sides of the equation:

2x = 180° - 45°

2x = 135°

Now, we divide both sides of the equation by 2 to solve for 'x':

x = 135° / 2

x = 67.5°

Thus, the measure of each of the other two angles is 67.5°.