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.

8 0

2 years ago

Explain TWO specific examples of how the development of cities and the construction of monuments resulted in the rise of mathema

Zinaida [17]

Mathematics and architecture are related, since, as with other arts, architects use mathematics for several reasons. Apart from the mathematics needed when engineering buildings, architects use geometry: to define the spatial form of a building; from the Pythagoreans of the sixth century BC onwards, to create forms considered harmonious, and thus to lay out buildings and their surroundings according to mathematical, aesthetic and sometimes religious principles; to decorate buildings with mathematical objects such as tessellations; and to meet environmental goals, such as to minimise wind speeds around the bases of tall buildings.

4 0

2 years ago