Whenever <u>two</u> or <u>more</u> lines <em>intersect </em>at a point, an <em>angle</em> is usually produced. And some of these angles formed may have <u>common </u>properties, and thus be <em>congruent</em>.
The appropriate reasons for the given <u>statements</u> in the question are given below:
STATEMENT REASON
1. <1 ≅ <2 <u>Vertical</u> <em>Angle</em> theorem
2. <1 and <2 are complementary
<2 and <3 are complementary <em>Congruent Complements</em> Theorem
3. <1 and <2 are supplementary
<2 and <3 are supplementary <u>Congruent</u> Supplements
4. <1 and <2 are right angles All<em> Right Angles</em> are Congruent
5. <1 ≅ <2,
<1 and <2 are supplementary If two angles are <u>congruent</u> and
<u>supplementary</u>, then each angle is
a <em>right angle</em>.
For more clarifications on the properties of complementary and supplementary angles, visit: brainly.com/question/14941189
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Answer:
Length of Shorter leg = 27 feet
Length of Longer leg = 36 feet
Length of Hypotenuse = 45 feet
Step-by-step explanation:
Given:
Let,
Length of Shorter leg = x,
According to the given condition we have
∴ Length of Longer leg = x + 9 feet
∴ Length of Hypotenuse = 2x - 9 feet
To Find:
Length of Shorter leg = ?
Solution:
Now In Right Angle Triangle, By Pythagoras theorem we have
substituting the given values we get
By using Identity (A ± B)² = A² ± 2AB +B² we get
Substituting x=27 we get
∴ Length of Longer leg = x + 9 =27 +9 = 36 feet
∴ Length of Hypotenuse = 2x - 9 = 2×27 -9 = 45 feet
Answer:
A change from 64 to 80 represents a positive change (increase) of 25%
Step-by-step explanation:
Answer:
a. 4/5
b. 150 and 120
Step-by-step explanation:
To find the scale factor first find two sides that correspond and have measurements. This is the length of each rectangles which are 50 and 40.
The equation for scale factor when scaling down is
SF = Smaller Length / Longer Length
When scaling up it is
SF = Longer / Smaller
We are scaling down so we plug in our numbers.
SF = 40 / 50
Solve for SF = .8 or 4/5.
For permimiter you add all four sides. Multiply the width of the larger pool by the scale factor. 25*.8 = 20
20 + 20 + 40 + 40 = 120
25 + 25 + 50 + 50 = 150