Download angle = complement

GEOMETRY
Complements
NAME_________________________
DATE __________ Per.___________
Proofs
1.
Fill in the table for each angle and its complement.
Angle Complement
Two angles are complementary angles
1°
89°
if
and only if the sum of their measures is 90°.
15°
90 –15 =
90 –30 =
45°
90 – ___ =
73°
x°
55°
90°–x°
90°–x°
2.
An angle is twice its complement.
a) Solve the problem using this equation:
x + 2x = 90
b) Solve the same problem again with this equation.
x = 2(90 – x)
c) What is the value of x in each solution? Are they the same?
d) Read the original problem again. Should the angle or its complement be the greater number?
Which solution is the complement?
each equation to its word problem and
3. Match
solve to find the angle and its complement.
algebraic techniques to solve each word
4. Use
problem. Find the angle and its complement if ...
x − 10 = 5 + (90 − x)
x = (90 − x) − 36
90 − x = x + 20
a) The complement is 20 more than the angle.
(HINT: angle + complement = 90°)
a) An angle is three times its complement.
complement = x
3x + x =
angle =
b) Five times an angle equals its complement.
angle = x
complement =
c) Twice an angle is three times is complement.
2(angle) = 3(complement)
b) The angle is 36° less than its complement.
c) 10° less than the angle is 5 more than the
complement.
5.
25° more than the angle is four times its complement. Find the angle and the complement.
HINT: angle + 25 = 4(complement)
angle =
complement =