Two angles of a triangle have the same measure. The measure of the third angle is 4°

less than twice the measure of each of the equal angles. Given that the sum of the three
angles of a triangle is always 180°, find each of the three angles.

If there are two angles of measure x, then we have

x + x + 2x-4 = 180

Now just find x, and you're almost done.

each of the equal angles ---- x

third angle = 2x - 4

so : x + x + 2x-4 = 180

continue

Let's denote the measure of each equal angle as 'x'. According to the information given, we have two equal angles measuring 'x' and a third angle measuring '2x - 4'.

The sum of the angles in a triangle is always 180°, so we can write the equation:

x + x + (2x - 4) = 180

Combine like terms:
4x - 4 = 180

Add 4 to both sides:
4x = 184

Divide both sides by 4:
x = 46

Now we can find the measure of each angle:
Equal Angle 1: x = 46°
Equal Angle 2: x = 46°
Third Angle: 2x - 4 = 2(46) - 4 = 92 - 4 = 88°

Therefore, the three angles of the triangle are: 46°, 46°, and 88°.

To find each of the three angles of the triangle, we can follow these steps:

Step 1: Let's represent the measure of each of the equal angles as "x". Since the two angles have the same measure, we can say that the first angle is "x" and the second angle is also "x".

Step 2: According to the given information, the measure of the third angle is 4° less than twice the measure of each of the equal angles. This can be expressed as: 2x - 4°.

Step 3: We know that the sum of the three angles of a triangle is always 180°. So, we can create the equation: x + x + (2x - 4°) = 180°.

Step 4: Simplify the equation and solve for x: 4x - 4° = 180°.

Step 5: Add 4° to both sides of the equation: 4x = 184°.

Step 6: Divide both sides of the equation by 4: x = 46°.

Step 7: Now that we have the value of x, we can substitute it back into the expressions for the angles to find their actual measures.

The first angle is x = 46°.
The second angle is also x = 46°.
The third angle is 2x - 4° = (2 * 46°) - 4° = 92° - 4° = 88°.

Therefore, the three angles of the triangle are 46°, 46°, and 88°.