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.
the answer can be 144 deg and 216 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°.