INSTRUCTIONS: Please solve and answer all problems listed with all steps include

Question

INSTRUCTIONS: Please solve and answer all problems listed with all steps included :)

1. Indicate which of the following angles below are acute and which are obtuse then give the complement and the supplement of each angle a) 10° b) 50° c) 160° d) 120 2. A searchlight rotates through one complete revolution every 4 seconds. How long does it take the light to rotate through 90°, through 180°? 3. An isosceles triangle is a triangle in which two sides are equal in length. The angle between the two equal sides is called the vertex angle, while the otheir two angles are called the base angles. If the vertex angle is 40°, what is the measure of the base angles? 4. An equilateral triangle is a triangle in which all three sides are equal. What is the measure of each angle in an equilateral triangle? Referring to a right triangle ABC with standard side names abc, with C = 90°, find the value of c given the following information a) If a = 4 and b = 3, find c. b) If a 8 and c17, findb c) If b-12 and c 13, find a 6. A surveyor is attempting to find the distance across a pond. From a point on one side of the pond he walks 25 yards to the end of the pond and then makes a 90° turn and walks another 60 yards before coming to a point directly across the pond from the point at which he started. What is the distance across the pond?

Explanation / Answer

1) acute angles are angles less than 90 degrees

and obtuse angles are angles greater than 90 degrees

acute angles are 10 degrees and 50 degrees

obtuse angles are 160 degrees , 120 degrees

finding complement and supplement of each angle

10 + x = 90

x = 80 degrees

10 +x = 180

x = 170

complement of 10 = 80 degrees

supplement of 10 = 170 degrees

complement of 50 = 40 degrees

supplement of 50 = 130 degrees

compement of 160 = -70 degrees

supplement of 160 = 20 degrees

complement of 120 = -30 degrees

supplement of 120 = 60 degrees

2) it takes 4 seconds to rotate 360 degrees

4 / x = 360 / 90

x = 1

so , it will take 1 second to rotate 90 degrees

4/x = 360/180

x = 2

it will take 2 seconds to rotate 180 degrees

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