Download 18 Angle2

Math with Measurements – Angle II
An equilateral triangle is a triangle with all
three sides of equal length. All of the angles
in an equilateral triangle are equal. For
example, the measure of each angle in the
triangle shown is 60o because the sum of the
angles in a triangle equals 180o. Since the
sum of the angles in any triangle is 180 o, all
equilateral triangles will have three 60 o
angles.
In equilateral or isosceles triangles, the sides opposite the equal angles
are also equal.
In a triangle, the largest angle is opposite the longest side and
the smallest angle is opposite the shortest side.
Exterior Angles of Triangles: An exterior angle of a triangle is equal to the sum of the
opposite interior angles. In the below diagram, ∠d = ∠a + ∠b, where a and b interior
angles and d is an exterior angle.
Calculate angles A, B and C
on the truss.
∠C = 90 – 55 = 35
∠A = 180 – 55 = 125
∠B = 55 – 34 = 21
Interior angles of a polygon are inside it. Each interior angle of a polygon measures
less than 180°. Exterior angles of a polygon are formed by extending one of two
adjacent sides. The sum of the angles of a polygon can be found by dividing the
1
polygon into triangles using the diagonals and then multiplying the number of triangles
by 180°. For example, a hexagon can be divided into 4 triangles, so the sum of the
angle measures is 4(180°) = 720°. Each interior angle of a regular hexagon is 120°, one
sixth of the total (720 ÷ 6 = 120).
An exterior angle is supplementary to its adjacent interior angle. Shown below are
interior and exterior angles of a regular pentagon and a regular hexagon.
A hexagon can be divided into 4 triangles, so the sum of the all
interior angle measures is 4(180°) = 720° and each interior angle is
720°÷ 6 = 120°.
Each exterior angle of a regular hexagon is 60 (180 – 120 = 60).
1. Which angles that you know would you use to estimate these angles (left to
right)?
A. 180°, 90°, 45°
B. 45°, 120°, 90°
C. 45°, 110°, 60°
D. 90°, 60°, 60
2
2. In the below quadrilateral, the two acute angles have measures of 35º and 70º. If
one obtuse angle measures 145º, what is the angle measure of the second
obtuse angle?
360 – 35 – 70 – 145 = 110
3. Find the measures of ∠A and ∠D.
130 + 50 + 2x + x = 360
180 = 3x
x = 60 = ∠D
∠A = 120
4. Which angle in the figure has a measure closest to 45°?
1.
2.
3.
4.
p
q
r
s
5. The figure above is a regular hexagon. What is the value of x?
60
3
6. In the figure at right, an arc of a circle with center P
has been drawn to cut the line at Q. Then an arc
with the same radius and center Q was drawn to cut
the first arc at R. What would be the size of angle
PRQ?
a. 30o
b. 45o
c. 60o
d. 75o
7. In a quadrilateral (a polygon with four edges (or sides) and four vertices or
corners), each of two angles has a measure of 115°. If the measure of a third
angle is 70°, what is the measure of the remaining angle?
a. 60°
b. 70°
c. 130°
d. 140°
8. The figure is not drawn to scale. ABC is an equilateral triangle. BCDE is a
trapezoid where BE // CD. ACD is a straight line. Find
9. WZYX is a trapezoid where WX // ZY. Find
WZY.
CBE.
60
63 (180 – 117)
4