Two angles of a quadrilateral measure 210° and 100°. The other two angles are in a ratio of 2:3. What are the measures of those two angles?
I know the four angles add to 360 deg. So the two unknowns are 50 deg together. 20 and 30 deg angles would give a ratio of 2:3, but what is the equation I would use to figure this using the ratio and the 50 deg?
Larger angle = X Deg.
Smaller angle = 2X/3 Deg.
X + 2X/3 = 360 - 310 = 50,
Multiply both sides by 3:
3X + 2x = 150,
5X = 150,
X = 30 deg.
2X/3 = 2/3(30) = 20 Deg.
To find the measures of the two unknown angles, let's assume that the angle measurements are 2x and 3x (as per the ratio of 2:3).
We know that the sum of all four angles of a quadrilateral is 360°. We also know the measurements of two angles, which are 210° and 100°. Therefore, we can set up the equation:
210 + 100 + 2x + 3x = 360
Combining like terms:
310 + 5x = 360
Subtracting 310 from both sides:
5x = 50
Dividing both sides by 5:
x = 10
Now, we can substitute the value of x back into the expressions for the two unknown angles:
2x = 2 * 10 = 20°
3x = 3 * 10 = 30°
Therefore, the measures of the two unknown angles are 20° and 30°.
To find the measures of the two unknown angles in a quadrilateral, we can follow these steps:
Step 1: Determine the sum of the known angles.
In this case, two of the angles measure 210° and 100°. So, their sum is 210° + 100° = 310°.
Step 2: Calculate the measure of the two unknown angles.
Let's assume the two unknown angles are x° and y°. We are given that they are in the ratio 2:3. This means that the measure of the first unknown angle, x°, is 2 times smaller than the measure of the second unknown angle, y°.
Using this information, we can set up the equation:
x = 2y
Step 3: Express the sum of the two unknown angles in terms of y°.
The sum of x° and y° should equal the remaining angle measure in the quadrilateral, which is 360° - 310° = 50°.
So, we can write the equation:
x + y = 50
Step 4: Solve the system of equations.
Now we have two equations:
x = 2y
x + y = 50
Substitute the value of x from the first equation into the second equation:
2y + y = 50
3y = 50
y = 50/3
y ≈ 16.67°
Now, substitute the value of y back into the first equation to find x:
x = 2(16.67)
x ≈ 33.33°
Therefore, the two unknown angles are approximately 33.33° and 16.67°.