## Measuring Angles Worksheet

Sherri Said:

Can a vertical angle measure 90 degrees? Or is it only right angles that measure 90 degrees?

1) The definition of right angle is, "It is the angle included between two straight lines which are perpendicular to each other. The measure of which is 90 deg"

2) The definition of Vertical angle is, "It is a pair of angles formed between two straight lines when they intersect at a point. The measurement of which can be anything from 0 to 180 deg"

3) Hence a measure of a vertical angle can be 90 degrees provided the two lines intersecting are perpendicular to each other at their point of intersection.

Jordan Said:

where can i find the answers to 1.3 measuring angles worksheet?

Probably the teacher's manual. That's an old edition and I don't think that's going to be online at the publisher's site. You can always try asking questions here on Y!A.

Wilma Said:

I need some input on these multiple choice questions for my math class...its a worksheet that's due today!!?

Haha i just covered this chapter in precal, i thought i would do one so yeah, number one is A.

Wanda Said:

always (by definitions of square, rectangle and rhombus)

--------------------------------------…

sorry can't understand what you want

--------------------------------------…

sometimes (the opposite angles of a rhombus are equal thus only if it is a square)

--------------------------------------…

sometimes (always congruent but perpendicular only if it is a square)

--------------------------------------…

never (the diagonals of a rhombus bisect each other perpendicularly so for the diagonals, the side is 13cm)

--------------------------------------…

you have AE = 9 cm (as the diagonals bisect each other perpendicularly)
and angle ABE = 42 deg (the diagonals bisect the angles between two subsequent sides)
thus the side = 9 / cos 42 = 12.1

--------------------------------------…

AC = 10 cm so BD = 10 cm (as the diagonals of a rectangle are congruent)
so by Pythagoras theorem, 10^2 = (x + 2)^2 + (x + 4)^2, thus x = -3 + (89)^(1/2) or -3 - (89)^(1/2) which is rejected.
thus the answer is EC + ED + CD = 5 + 5 + 1 + (89)^(1/2) = 11 + (89)^(1/2)
i have triple checked my answer. check if you have typed the question correctly
this is the method though.

--------------------------------------…

AC = 20
BC = AD = 12 = 2x + y
by Pythagoras theorem, you get 3x - y = 12
thus x = 4.8 and y = 2.4

--------------------------------------…

I'll tell you how to proceed as the value of RC is not typed.

the subsequent angles at the point of intersection of the diagonals are supplementary.
draw the perpendicular bisectors of the sides, they bisect the angles at the center X.
let them intersect RE, EC, CT and RT at L, M, N and O
now, RX = EX = CX = TX = RC/2 and angle RXO = 30 deg and angle RXL = 60 deg
Use trigonometry to find RO (=RX cos30) and RL (=RX cos60).
RT = 2 RO = EC
RE = 2 RL = CT

I will deal the same problem using the property of parallel lines (this is faster)

after drawing the perpendicular bisectors, LN and MO you see that they are parallel to sides EC and CT respectively, and by corresponding angle property of parallel lines and transverse lines, angle RXO = angle RCT = 30 and angle RCE = 60 deg by complementary angle property of angles RCT and RCE
again using trigonometry, RT = EC = RC cos30 and RE = CT = RC cos60
you may use pythagoras theorem in some places, but trigonometry is easier.

--------------------------------------…

the side of the square = diagonal / cos45 = 2^(1/2) * 18
thus the perimeter = 72 * 2^(1/2) = 101.8
as for the rhombus, draw the diagonal RO, they bisect perpendicularly at X. now angle RHX = 30 deg thus RH = HX / cos30 = 2 * 9 / 2^(1/2) = 6 * 3^(1/2)
thus the perimeter = 24 * 3^(1/2) = 41.5
clearly the rhombus has the smaller perimeter.

Mike Said:

The measures of an angle and its supplement differ by 44º. Find the measure of the angles?

x + x + 44 = 180.
2x+ 44 = 180. x = 68.

Edit: The girl below is wrong. Supplementary angles are angles = 180, not 90.

Dwayne Said:

A couple Geometry questions I just can't get?

10.
the sum of the angles in a polygon can be expressed as 180(n-2) where n is the number of sides. For a 12-sided polygon:

x=180(12-2)
x=1,800º

Since it is regular, that works out to be 150° for every interior angle. The ext. angle is 180-int, which is 30°.

10.
Exterior angle is 180-int. To find the missing interior angle:

ext=180-int
123=180-int
int=57°

Then, we go back to this formula:

180(n-2)

Which, for a triangle, is 180° total. We are given 58.5° and we found 57°, so for them to all equal 180° the 3rd one must be 64.5°.

7.
Since we already know that the sum of the angles in a triangle is 180°, the sum of y and z must be 180°-10°, or 170°. Therefore:

y+z=170
z=170-y
y=170-z

Ron Said: