Using a system of equations, it is found that Wilma is 50 years old and Yvonne is 10 years old.
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
- Variable y: Yvonne's age.
Wilma is 5 times as old as yvonne, hence:
x = 5y.
In ten years, yvonne's age will be a third of wilma's age, hence:
Since x = 5y:
3y + 30 = 5y + 10
2y = 20.
y = 10.
Then:
x = 5y = 5 x 10 = 50.
Wilma is 50 years old and Yvonne is 10 years old.
More can be learned about a system of equations at brainly.com/question/24342899
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Explanation:
<u>Statement 2</u>:
Angle J is congruent to itself
<u>Reason 2</u>:
Reflexive property of congruence
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<u>Statement 3</u>:
ΔHIJ ~ ΔGHJ
<u>Reason 3</u>:
SAS similarity theorem
_____
The sides given as proportional (having the same ratio) are corresponding sides in the two triangles. The first pair of sides (HJ, GJ) are named by the first and last letters of the triangle names, so correspond. The second pair of sides (IJ, HJ) are named by the last two letters of the triangle names, so correspond.
The angle between these corresponding sides is the one at the vertex whose name is the point shared by the sides. In the first triangle, the two sides of interest are HJ and IJ, which share the point at J. Thus angle J is the angle between these two sides. In the second triangle, the two sides of interest are GJ and HJ, which share the point at J. Hence angle J is the angle between these two sides, also.
So, we have corresponding sides that are proportional and the angle between them that is congruent (to itself). This allows us to invoke the SAS theorem for triangle similarity.
What do you need help with?
Answer:
x + 49 + 28 = 180
Step-by-step explanation:
The angle adjacent to x on the left is vertically opposite 49° and is congruent.
The 3 angles then lie on a straight line and sum to 180° , that is
x + 49 + 28 = 180
