Answer:
Step-by-step explanation:
The picture given in the exercise shows a Quadilateral which has an angle whose measure is unknown.
By definition, the sum of the interior angles of a quadrilateral is 360 degrees.
Knowing this, you can write the following equation:
Finally, you must solve for the angle "x" in order to calculate its measure.
This is:
So we know that point-slope form is as follows:
The points ( and
correspond to the point given and m is representing the slope. So we plug in what the question gives us:
<------ Point-slope form
Now we can take this form and simplify to give us the slop-intercept form:
<----- Slope-intercept form
An equilateral triangle with side length 6 is similar to an equilateral triangle with side length 15
<em><u>Solution:</u></em>
Given that we have to find whether the polygons are similar
<em><u>An equilateral triangle with side length 6</u></em>
An equilateral triangle is a triangle in which all three sides are equal
All three internal angles are also congruent to each other and are each 60°
Let ABC be a equilateral triangle with side length 6
Since all three sides are equal,
AB = 6
BC = 6
CA = 6
Also, angle A = 60 degrees and angle B = 60 degrees and angle C = 60 degrees
<em><u>An equilateral triangle with side length 15</u></em>
Let XYZ be a equilateral triangle with side length 15
Since all three sides are equal in equilateral triangle,
XY = 15
YZ = 15
ZX = 15
Also, angle X = 60 degrees and angle Y = 60 degrees and angle Z = 60 degrees
Two triangles are similar if they have the same angles and the side lengths are proportional.
Since,
Also,
Angle A = angle X = 60 degrees
Angle B = angle Y = 60 degrees
Angle C = angle Z = 60 degrees
Since equilateral triangles all have the same angles, and all side lengths are equal, any two equilateral triangles must be similar.