Two of four angles of a quadrilateral are equal, each being equal to 120°. The ratio of the other two angles is 2:3. Find these two angles.
So far you have 120° + 120° or 240° for the two equal angles, which leaves
360-240 or 120° for the remaining two angles.
But they are to be in the ratio of 2:3
let the smaller be 2x and the larger be 3x
2x+3x = 120
solve for x, and sub back into 2x and 3x.
120 + 120 + 2x + 3x = 360.
Solve for x, 2x, and 3x.
To find the other two angles, let's consider the information provided.
We are given that two of the four angles of the quadrilateral are equal to 120°. Let's call these angles x and y.
So, x = y = 120°.
We are also given that the ratio of the other two angles is 2:3. Let's call these angles a and b.
So, a/b = 2/3.
To find the values of a and b, we can use the fact that the sum of the angles in a quadrilateral is always 360°.
Therefore, we have the equation: x + y + a + b = 360°.
Substituting the given values, we have: 120° + 120° + a + b = 360°.
Simplifying the equation, we get: 240° + a + b = 360°.
Now, we can substitute the ratio a/b = 2/3 into the equation.
2/3 can be expressed as 2x/3x, where x is a common factor.
Therefore, we have: 240° + 2x + 3x = 360°.
Combining like terms, we get: 5x + 240° = 360°.
Subtracting 240° from both sides, we get: 5x = 120°.
Dividing both sides by 5, we get: x = 24°.
Now, we can substitute x = 24° into the ratio a/b = 2/3.
So, a/b = 2/3 can be written as a/24 = 2/3.
Cross-multiplying, we get: 3a = 2 * 24.
Simplifying, we get: 3a = 48.
Dividing both sides by 3, we get: a = 16°.
Now, we can find the value of b by subtracting the sum of the other angles from 360°.
b = 360° - (x + y + a).
Substituting the values, we have: b = 360° - (120° + 120° + 16°).
Simplifying, we get: b = 360° - 256°.
Therefore, b = 104°.
To summarize, the two angles a and b are 16° and 104°, respectively.