An isosceles triangles, such that the vertical angle is 4times the size of the base angle.what is the size of the base angle with illustration
Let x be the size of the base angle. Since the vertical angle is 4 times the size of the base angle, the vertical angle is 4x.
In an isosceles triangle, the sum of the base angles is equal to 180 degrees minus the vertical angle:
x + x + 4x = 180
6x = 180
x = 30
So the size of the base angle is 30 degrees.
Here's a simple illustration:
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4x=120/ \
/ \
/________\
x=30 x=30
To find the size of the base angle in an isosceles triangle where the vertical angle is 4 times the size of the base angle, we can follow these steps:
Step 1: Let's assume the size of the base angle to be 'x'.
Step 2: According to the problem, the vertical angle is 4 times the size of the base angle. So, the vertical angle would be 4x.
Step 3: Since we know that the sum of the angles in a triangle is 180 degrees, we can write the equation: base angle + base angle + vertical angle = 180.
Step 4: Substitute the values we have: x + x + 4x = 180.
Step 5: Simplify the equation: 6x = 180.
Step 6: Solve for x: x = 180/6 = 30.
Step 7: Therefore, the size of the base angle is 30 degrees.
Illustration:
In an isosceles triangle, the base angles are always equal. Let's assume the base is represented by the line segment AB, and the vertex opposite the base is C. The base angles are formed by the lines AC and BC. Let the base angle (x) be 30 degrees. Then, the vertical angle (4x) would be 120 degrees. The isosceles triangle would look like this:
C
/ \
/ \
/ \
/__x___\
A B
In this illustration, angle CAB = angle CBA = 30 degrees, and angle ACB = 120 degrees.
To find the size of the base angle in an isosceles triangle where the vertical angle is 4 times the size of the base angle, we can use some algebraic equations. Let's assume the size of the base angle is 'x' degrees.
According to the given information, the vertical angle is 4 times the size of the base angle. Therefore, the vertical angle can be expressed as 4x degrees.
Now, in any triangle, the sum of all angles is always 180 degrees. In an isosceles triangle, we have two congruent base angles and one vertical angle.
So, we can form the following equation:
x + x + 4x = 180
Now, let's solve this equation to find the value of 'x':
6x = 180 (combining like terms)
x = 180 / 6 (dividing by 6)
x = 30
Therefore, the size of the base angle (illustrated as 'x') in the isosceles triangle is 30 degrees.