Answer:
1) The square ABCD was dilated to form square A'B'C'D' using a scale factor of 1/2
2) The pair of polygons is not similar because their corresponding sides are not proportionals.
Step-by-step explanation:
1) Scale factor: f=?
f=Final dimension / Initial dimension
f=A'B'/AB=B'C'/BC=C'D'/CD=A'D'/AD
f=2/4
Simplifying the fraction dividing the numerator and denominator by 2:
f= (2/2) / (4/2)
f=1/2
2) Let's check the proportion between their corresponding sides:
AM/A'M'=(11 ft)/(9.4 ft)=1.17
HT/H'T'=(11 ft)/(9.4 ft)=1.17
HM/H'M'=(10 ft)/(8.4 ft)=1.19
AT/A'T'=(10 ft)/(8.4 ft)=1.19
AM/A'M'=HT/H'T'=1.17 but different to 1.19=HM/H'M'=AT/A'T'
Then, the pair of polygons is not similar
Supplementary angles are angles that add up to 180 degrees
Answer = 180 - 142 = 38 degrees
Answers: ∠a = 30° ; ∠b = 60° ; ∠c = 105<span>°.
</span>_____________________________________________
1) The measure of Angle a is 30°. (m∠a = 30°).
Proof: All vertical angles are congruent, and we are shown in the diagram that angle A — AND the angle labeled with the measurement of 30°— are vertical angles.
2) The measure of Angle b is 60°. (m∠b = 60<span>°).
Proof: All three angles of a triangle add up to 90 degrees. In the diagram, we can examine the triangle formed by Angle A, Angle B, and a 90</span>° angle. This is a right triangle, and the angle with 90∠ degrees is indicated as such (with the "square" symbol). So we know that one angle is 90°. We also know that m∠a = 30°. If there are three angles in a triangle, and all three angles must add up to 180°, and we know the measurements of two of the three angles, we can solve for the unknown measurement of the remaining angle, which in this case is: m∠b.
90° + 30° + m∠b = 180<span>° ;
</span>180° - (<span>90° + 30°) = m∠b ;
</span>180° - (120°) = m∠b = 60<span>°
</span>___________________________
Now we need to solve for the measure of Angle c (<span>m∠c).
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All angles on a straight line (or straight "line segment") are called "supplementary angles" and must add up to 180</span>°. As shown, Angle c is on a "straight line". The measurement of the remaining angle represented ("supplementary angle" to Angle c is 75° (shown on diagram). As such, the measure of "Angle C" (m∠c) = m∠c = 180° - 75° = 105°.
Reference angle of -3 radians is α= - 171° 53 min 15 sec .
We know the formula for calculating circular arc
Let l=circular arc which ic according to central angle of the circle α
l=((2R π)/360)α Let l=1 radian and R=1 (unit circle with radius R=1)
1= ((2π)/360)α => α= 360/(2π)= 180/π= 57° 17 min 45sec
Angle of the 1 radian is equal to angle 57° 17min 45sec
According to this
angle of the -3 radians = -3 ( 57° 17min 45sec) = - 171° 53min 15sec
when you count in the clockwise direction.
Good luck!!!
-4p+9=-5
-9 -9
-4p=-14
divide the entire thing by -4
p=3.5
Hope this helps!
