angle bac measures 56°. what is the measure of angle bdc? 28° 34° 56° 112° This is a topic that many people are looking for. bluevelvetrestaurant.com is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, bluevelvetrestaurant.com would like to introduce to you Calculating Angle Measures. Following along are instructions in the video below:
Video is on calculating angle measures. We can use what we learned about angles from from the vocabulary exploration activity to calculate angle measures. Lets review.
Some of these vertical angles are non adjacent angles that are formed by intersecting lines and vertical angles are congruent so in the diagram below angles. One and two are vertical angles. So angle.
1 is congruent to angle 2 and 3 4. Are vertical angles. So angle.
3 is congruent to angle 4. Complementary angles are two angles with measures that have a sum of 90 degrees so in the diagram below angles one and two are adjacent complementary angles. Remember adjacent means theyre right next to each other so the measure of angle.
One plus. The measure of angle two equals 90. And you know that theyre 90 because they actually show you this little red box here this makes that a right angle angles.
A and b are non adjacent complementary angles. Because 65 plus 25 is equal to 90 so complementary angles add up to 90 degrees. Supplementary angles are two angles.
With measures that have a sum of 180 degrees in the diagram below three and four angles three and four are not only supplementary angles. But they also form a linear pair since they are adjacent to each other angles. 3 4.
Together make a straight line so they add up to 180 so theyre supplementary. But because they share this ray they are adjacent to each other and recall that thats what we call a linear pair angles. P.
And q are also supplementary angles. Since 120 plus 60 is equal to 180. So those are two angles.
Add up to 180 degrees. An angle bisector oops. An angle.
Bisector is array that creates two congruent angles so in the diagram below ray yw bisects angle xyz so angle xy w. Is congruent to angle w y z. And theyve noted that by showing that theyre both equal to 80 degrees.
So an angle bisector cuts. An angle into two congruent angles perpendicular lines form right angles and right angles. Measure 90 degrees.
So in the diagram below. If line pr is perpendicular to line sq. And if youre not familiar with that this is the symbol for perpendicular so pr is perpendicular to sq then it creates for right angles.
Angle p. Tq angle. Qt r angle rts and angle stp all of those right angles.
And each measures 90 degrees. So lets use some of these to solve a couple of problems here. And i think i have three examples first one says lets find the measure of angle q r t.
So here we have line qr s which is a straight line and rate r t coming out of it so these actually form a linear pair so they are supplementary and add up to 180 degrees. So i can say the measure of angle qr t. Plus.
The measure of angle t are s is equal to 180 so im given an algebraic expression for q r t. Which is 9x and an algebraic expression for t rs. Which is 3x that equals 180.
And from here. I can just go ahead and solve this algebraically and dividing both sides by 12 x. Is equal to 15.
But im not done i dont this isnt like algebra where we just stop when we find x we have to plug it back in so the measure of angle qr t. Is 9x so the measure of qr t. Which is what i have to find is nine times 15 or nine times 15 is 135.
So angle qr t. Is 135 degrees heres another example here we have two adjacent angles. And it says if the measure of angle.
Ma r is equal to 124. We need to find x so i know that the measure of angle. M mac.
Just this angle right here plus the measure of angle c. Ar is equal to 124. Because they told.
Me. That ma. C.
Is 6x. Minus 11. C.
Ar. Is 4x minus 25. And once again.
Im back in algebra land. So 10x minus. 36.
Equals. 120. For adding 36 to each side gives me 160 x.
Equals. 16. And lets go back.
And read the problem. So i did just have to find x. So im finished with that one and one last example here it says if raabe bisects angle dac.
I need to find x well if a b bisects this angle. Which notice. It has this little box in the corner.
So i know that the measure of angle dac is 90 degrees. Its a right angle. I know that these two angles are the same because that that ray bisects.
Them so i can say 2 times 7x minus 4. Equals 90 degrees. Because that ray bisects.
A 90 degree angle. I could also say i know that half of 90 is 45. So i could go ahead and say 7x minus.
4. Equals. 45.
Which is the same thing i get if i divide both sides of this by 2. But im just going to go ahead and distribute and add 8 to both sides and dividing both sides by 14 x. Is equal to 7.
So in this video. We took a look at how to calculate angle measures. We reviewed some of the concepts and some of the terminology and definitions with regard to angles and their measures and saw how to use them in three specific problems.
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