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Math 154 — Rodriguez
Angel — 3.3
Geometric Problems
You got through the applications from section 3.2 so those should seem a breeze…why?
Setting up the equation is based on a geometry formula.
Here is a list of the formulas you’ll need:
complementary angles: two angles whose sum is 90°
supplementary angles: two angles whose sum is 180°
angles in a triangle: sum of the three angles is 180°
angles in an isosceles triangle: two angles have the same measure
angles in a quadrilateral: sum of the four angles is 360°
angles in a parallelogram: opposite angles have the same measures
perimeter of a rectangle: P = 2l + 2w
Still expect you to:
a)
b)
c)
d)
Define any variable you use.
Write an equation that represents the relationships in the word problem.
Solve the equation.
Answer the question.
Example 1: Angles A and B are supplementary. Angle B is 25° less than angle A. Find the
measures of angle A and angle B.
a) Define:
measure of angle A =
measure of angle B =
b) Equation: supplementary angles: sum is 180°
measure angle A + measure angle B = 180°
c) Solve:
d) Answer:
angle A __________; angle B _________
Example 2: The measure of one angle of a quadrilateral is three times the smallest; the third
angle is 10° greater than the smallest angle; and the fourth angle is 20° less than
twice the smallest. Find the measures of the four angles.
Define:
measure of the smallest angle =
measure of 2 nd angle (the ‘one’ angle) =
measure of 3 rd angle =
measure of 4 th angle =
Equation:
sum angles in a quadrilateral is 360°
Solve:
Answer:
You try…
Example 3: The perimeter of a rectangle is 3 feet more than twice the width. If the perimeter
is 60 feet, what are the dimensions of the rectangle?
Example 4: Two angles are complementary. The measure of angle A is 6 less than twice the
measure of angle B. Find the measure of each angle.
Example 5: One angle of a triangle is 20° greater than the smallest. The third angle is twice
the smallest. Find the measures of the three angles.
Angel — 3.3
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