Suppose the bisector of an angle divides the angle into 2 angles, each of which has a measure of 15 degrees less than the complement of the angle. What is the measure of the original angle?

Question

Suppose the bisector of an angle divides the angle into 2 angles, each of which has a measure of 15 degrees less than the complement of the angle. What is the measure of the original angle?

Answer 1

let the angle be 2x

then the bisected angle is x
the complement of the original angle is 90-2x

"..each of which has a measure of 15 degrees less than the complement of the angle"
---> x = 90-2x - 15
3x = 75
x = 25

so the original angle, defined as 2x, is 50°

check:
complement of 50° is 40°
the bisected angle is 25°
is 25 less than 40 by 15 ? , YES

Answer 2

given an equilateral teiangle abc of side 3cm. f is the symmetric of c with respect to b and g is the symmetric of b with respect to c

drow the figure

Answer 3

Let's assume that the measure of the original angle is "x" degrees.

According to the given information, each of the two angles formed by the bisector is 15 degrees less than the complement of the original angle.

The complement of an angle is the angle that, when added to the original angle, equals 90 degrees.

So, the complement of the original angle is 90 - x degrees.

Now, we can set up an equation to represent the given information:

x = (90 - x) - 15

Simplifying this equation:

x = 90 - x - 15

Combining like terms:

x = 75 - x

Adding x to both sides:

2x = 75

Dividing both sides by 2:

x = 37.5

Therefore, the measure of the original angle is 37.5 degrees.

Answer 4

To solve this problem, let's start by defining some variables. Let's say that the measure of the original angle is x degrees.

Now, let's consider the complement of the original angle. The complement of an angle is the angle that, when added to the original angle, forms a 90-degree angle (a right angle). Therefore, the complement of the original angle is 90 - x degrees.

According to the problem, the bisector of the angle divides it into two angles, each of which has a measure of 15 degrees less than the complement of the angle. So, each of these angles can be expressed as (90 - x) - 15 = 75 - x degrees.

Since the bisector divides the original angle into two angles, their sum should be equal to the original angle. Therefore, we can write the equation:

(75 - x) + (75 - x) = x

Simplifying the equation, we have:

150 - 2x = x

Now, let's solve for x:

3x = 150
x = 50

Hence, the measure of the original angle is 50 degrees.