Decompose angles

Toothy the crocodile wants to eat a delicious chicken.His mouth is open to an angle of  30∘. He needs to open his mouth to an angle of 55∘ for the chicken to fit.

What is the measure of the additional angle Toothy’s mouth needs to open so he can eat the chicken?

What is the measure of ∠x?

When Ranim started karate, her highest kick went  110∘ from the ground. Her instructor asked her to practice until her highest kick goes 155∘from the ground.

Which equation will tell us the measure of the additional angle, a,  that Ranim’s kick needs to go to reach 155∘ from the ground?

Choose 1 answer:

Louie the oyster wants to show all of the other oysters what a nice pearl he has made. He opens up his shell to an angle of 22∘, 1$0$but they still can’t see the pearl.

Louie opens his shell 37∘ more, and then all of his friends are amazed at the beautiful pearl.

How many total degrees did Louie open his shell?

What is the measure of ∠y?

Hint: $\angle x$is a right angle.

What is the measure of ∠y?

Nuha is going through a revolving door that needs to rotate 160∘ to allow her to pass through. The wind pushed the door around 40∘. Nuha needs to push it the rest of the way.

Which equation will tell us the measure of the additional angle, a, that Nuha needs to push the door before she can get out?

Choose 1 answer:

A stunt man wants to drive a car off a ramp at an angle of 35∘ from the ground.He already has a ramp with an angle of 15∘. He plans to add a second ramp on top to increase the angle to 35∘.

What angle measure does the second ramp need to have?

What is the measure of ∠x?

What is the measure of ∠y?

Which equation will tell us the measure of ∠x?

Choose 1 answer:

Kayla is working on a new snowboard trick.Her best trick used to be a 360∘ full-circle turn, but now she can turn further by an additional 180∘ half-circle.

What is the angle measure of her total turn now?

What is the measure of ∠y?

Hint: $\angle z$ is a straight angle.

What is the measure of ∠z?

Hint: $\angle y\; is\; a\; right\; angle.$

Which equation will tell us the measure of ∠x?

Hint:$\angle y\; is\; a\; straight\; angle.$

Choose 1 answer:

In order to get toys from under the couch, Mom lifted up the couch to an angle of 31∘. The kids still could not reach the toys. Then, she lifted it up another 15∘ and the kids pulled out a bouncy ball, a foam dart, three rubber bands, and a Lego.

What was the measure of the total angle Mom lifted the couch?

What is the measure of ∠w?

What is the measure of ∠x?

Which equation will tell us the measure of ∠w?

Hint:$\angle x\; is\; a\; right\; angle.$

Choose 1 answer:

Stephanie was going through a revolving door that needs to rotate 170∘ to allow her to pass through.She pushed the door around 105∘ but then the door got stuck. Her friend helped her push the door another 15∘ but it is still not open far enough.

What is the measure of the additional angle that the door needs to turn before Stephanie can get out?

What is the measure of ∠x?

What is the measure of ∠x?

Which equation will tell us the measure of ∠x?

Choose 1 answer:

Arush is reading a pop-up book. When the book is open to an angle of 105∘ the wizard’s wand is waving to the left. When the page is opened 45∘ more, the wizard’s wand waves to the right.

What is the angle of the page when the wizard’s wand waves to the right?