Question

Промінь МF поділяє разгорнутий кут EMH у відношенні 1:2 .Знайдіть ці кути

Answer 1

Развернутый угол равен 180⁰.
УголЕМF=180⁰/(1+2)=180⁰/3=60⁰
УголFMH=180⁰-60⁰=120⁰

Answer 2

Calculation of Angles in a Triangle

To find the angles of a triangle when the ratio of one angle to another is given, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

Let's assume that the three angles of the triangle are A, B, and C, and the given ratio is 1:2 for angle A to angle B.

According to the given information, we can write the equation:

A/B = 1/2

To solve for the angles, we need to find the value of angle B in terms of angle A. We can do this by rearranging the equation:

B = 2A

Now, we can substitute the value of angle B in terms of angle A into the equation for the sum of the angles in a triangle:

A + 2A + C = 180

Simplifying the equation:

3A + C = 180

To find the values of angles A and C, we need one more equation. Since the ratio of angle A to angle B is given as 1:2, we know that the sum of the ratios is 3:

1 + 2 = 3

Therefore, the ratio of angle A to the sum of all three angles is 1:3. We can use this ratio to find the value of angle A:

A = (1/3) * 180

Simplifying:

A = 60 degrees

Now, we can substitute the value of angle A into the equation we derived earlier to find angle B:

B = 2A = 2 * 60 = 120 degrees

Finally, we can find angle C by substituting the values of angles A and B into the equation for the sum of the angles in a triangle:

3A + C = 180

3 * 60 + C = 180

C = 180 - 180 = 0 degrees

Therefore, the angles of the triangle are:

Angle A = 60 degrees Angle B = 120 degrees Angle C = 0 degrees

Please note that an angle of 0 degrees is not physically possible in a triangle, so it is likely that there is an error in the given information or calculation.