Below I have included an image that has the measure of all of the angles on it.
We can find the measures of the angles here due to the laws about complimentary angles. A pair of complimentary angles can be formed when 2 lines are perpendicular, and when added together, will always equal 90. The pair are the angles that are not directly adjacent from each other. In this figure, "x" and "(4x-10)" are a pair. According to another law, opposite angles, or adjacent angles, will always be equal to each other. Using the logic above is how we can find the measure of all angles.
Since one angle has a box, we know the lines are perpendicular, and that the laws of complimentary angles apply. We can also use that to see that the angle diagonal from it is equal to 90.
To solve for the other measures, we need to add the 2 equations together and set them equal to 90 (because of that law we talked about before).
x+(4x-10)=90
5x-10=90
+10+10
5x=100
/5 /5
x=20
Now that we know x equals 20, we can substitute that value in and solve.
x=20
=(4x-10)
=(4*20-10)
=(80-10)
=70
We also know this is correct because 20 and 70 equal 90.
We can find the measures of the angles here due to the laws about complimentary angles. A pair of complimentary angles can be formed when 2 lines are perpendicular, and when added together, will always equal 90. The pair are the angles that are not directly adjacent from each other. In this figure, "x" and "(4x-10)" are a pair. According to another law, opposite angles, or adjacent angles, will always be equal to each other. Using the logic above is how we can find the measure of all angles.
Since one angle has a box, we know the lines are perpendicular, and that the laws of complimentary angles apply. We can also use that to see that the angle diagonal from it is equal to 90.
To solve for the other measures, we need to add the 2 equations together and set them equal to 90 (because of that law we talked about before).
x+(4x-10)=90
5x-10=90
+10+10
5x=100
/5 /5
x=20
Now that we know x equals 20, we can substitute that value in and solve.
x=20
=(4x-10)
=(4*20-10)
=(80-10)
=70
We also know this is correct because 20 and 70 equal 90.