The measure of an angle is seventeen times the measure of a complementary angle. What is the measure of each angle?

1 answer:

7 0

First, write an equation system for the problem
For example, x represents the first angle and y represents the second angle
An equation for "the measure of an angle is seventeen times the measure of a complementary angle" is
∴ x = 17y
The sum of complementary angle is 90°. It can be written as
∴ x + y = 90°

Second, use subtitution method to find the value of x and y
Subtitute x with 17y
x + y = 90°
17y + y = 90°
18y = 90°
y = 90°/18
y = 5°

Subtitute y with 5°
x = 17y
x = 17(5)
x = 85°

The measure of each angle is 5° and 85°

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If the measure of a triangle are in the ratio 2:5:5. What is the measure of the angle

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Your answer is 75°, 75°, and 30°
Because you know that angles in a triangle equal 180°, you can find what 1 in terms of the ratio is by adding 2, 5, and 5, and then dividing 180 by that value. 2 + 5 + 5 = 12, so 180 ÷ 12 = 15.
Now that you know that 1 in terms of the ratio is 15, you can multiply 15 by the ratio values, so
15 × 2 = 30°
15 × 5 = 75°
15 × 5 = 75°

I hope this helps!

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