Hello!

We know that the sum of the three angles of a triangle is equal to 180 degrees. This can be represented using the following formula:

A1 + A2 + A3 = 180

With this knowledge, we can successfully find the missing measurements.

We’ll begin with the large right triangle. Because it is a right triangle, we know that one of its angles is equal to 90 degrees. We are also given that its second angle has a measure of 65 degrees. Insert this information into the formula above and combine like terms:

(90) + (65) + A3 = 180
155 + A3 = 180

Now subtract 155 from both sides of the equation:

A3 = 25

We have now proven that the third angle has a measure of 25 degrees. Looking at the provided image, you’ll notice that this 25 degree angle is adjacent to the 80 degree angle. We can add these neighboring angles to find one of the missing angles of the medium triangle:

25 + 80 = 105

We have now proven that this larger angle has a measure of 105 degrees. Looking again at the provided image, you’ll notice that this triangle also contains a 50 degree angle. Using the “three-angles” formula, we can find the remaining angle of the medium triangle. Insert any known values and combine like terms:

(105) + (50) + A3 = 180
155 + A3 = 180

Now subtract 155 from both sides of the equation:

A3 = 25

We have now proven the third angle of the medium triangle to have a measure of 25 degrees. Consequently, we now have now proven two of the three angles of the smallest triangle. Again using the “three-angles” formula, we can find the measure of the missing angle (x). Insert any known values (using the variable “x” to represent the missing angle) and combine like terms:

(25) + (25) + (x) = 180
50 + x = 180

Now subtract 50 from both sides:

x = 130

we have now proven that the missing angle (x) has a measure of 130 degrees.

I hope this helps!
second angle which has a value of 65 degrees.

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2 years ago