In ∆FDH, there are two slash marks in two of its legs. This indicates that this triangle is isosceles. If a triangle is isosceles, then it will have two congruent sides and therefore have two congruent angles.
In ∆FDH, angle D is already given to us as the measure of 80°. We can find out the measure of the other angles of this triangle by using the equation:
80 + 2x = 180
Subtract 80 from both sides of the equation.
2x = 100
Divide both sides by 2.
x = 50
This means that angle F and angle H in ∆FDH both measure 50°.
Now, moving over to the next smaller triangle in the picture is ∆DHG. In this triangle, there are also two legs that are congruent which once again indicates that this triangle is isosceles.
First, we have to solve for angle DHG and we do that by using the information obtained from solving for the angles of the other triangle.
**In geometry, remember that two or more consecutive angles that form a line will always be supplementary; the angles add up to 180°.**
In this case angle DHF and angle DHG are consecutive angles which form a linear pair. So, we can use the equation:
Angle DHF + Angle DHG = 180°
50° + Angle DHG = 180°.
Angle DHG = 130°.
Now that we know the measure of one angle in ∆DHG, we can use the same method as the previous step for solving the missing angles. Use the equation:
130 + 2x = 180
2x = 50
x = 25
The other two missing angles of ∆DHG are 25°. This means that the measure of angle 1 is also 25°.
Solution: 25°
Answer:
No
Step-by-step explanation:
Apply the distributive property to 5(2x - 3y):
Multiply 5 by each term inside the parentheses.
5(2x - 3y) = 10x - 15y
The other expression is 10x - 10y.
The terms 10x in both expressions are equal.
Since the term -15y is not equal to the term -10y, the expressions are not equivalent.
Answer:parallelogram
Step-by-step explanation: If one pair of opposite sides of a quadrilateral are equal and parallel, then the quadrilateral is a parallelogram
Answer:
Good Luck
Step-by-step explanation:
If 2 boxes remain empty, it means that we put all three balls in one single box.
Suppose the full box is box number 1. For each ball, we have three choices - we may put it in box number 1, 2 or 3. This means that each box has a 1/3 chance of receiving each ball.
So:
- we choose box 1 for ball 1 - that's a 1/3 chance
- we choose box 1 for ball 2 - that's a 1/3 chance
- we choose box 1 for ball 3 - that's a 1/3 chance
So, the probability of putting all balls in box 1 is
But this is the probability of putting all ballx in box 1, and you can repeat this logic for box 2 and 3.
So, the probability of putting all balls in one single box is 1/27 for each box, for a total of
