The diagram shows line j interception with Lion k and some of the measure angles move the numbers into the box to show the volume of x and y quotation x + 30 quotation degrees k 1 28° quotation 3y + 1°j
The diagram shows line j intersecting with line k and some of the measured angles.
The angle x is given as x + 30°
The angle k is given as 28°
The angle y is given as 3y + 1°
The angle j is not given.
We need to find the values of x and y.
From the diagram, we can see that angles x and k are supplementary angles, which means they add up to 180°.
Therefore, x + 30° + 28° = 180°
x + 58° = 180°
x = 180° - 58°
x = 122°
Next, we can find the value of y by noticing that angles y and j are vertical angles, which means they are equal.
Therefore, y = j
Now, we know that y + y + 1° = 180° (because they are a linear pair)
2y + 1 = 180
2y = 179
y = 179 / 2
y = 89.5
So, x = 122° and y = 89.5°.
You sure
Let's double-check the values for x and y:
Given:
x + 30° = k (as x and k are supplementary)
k = 28°
3y + 1° = j (as y and j are vertically opposite angles)
From the information given:
k = 28°
From the supplementary property of x and k:
x + 30° = 180° - k
x + 30° = 180° - 28°
x + 30° = 152°
x = 152° - 30°
x = 122°
Now, from the relationship between y and J:
3y + 1° = j
3y + 1° = j
3y + 1° = j
3y = j - 1°
y = (j - 1°) / 3
Now we substitute the known values:
j = 3y + 1°
j = 3(89.5) + 1°
j = 268.5 + 1°
j = 269.5°
Therefore, the final values are:
x = 122°
y = 89.5°
j = 269.5°
So, the values have been recalculated, and these are the correct values for x, y, and j based on the given information.