Angles around a point

Difficulty Stretch · Set ecpltr

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1
5 angles meet at a point. 4 of them are 38°, 37°, 51°, 53°. What is the last one, in degrees?
2
5 angles meet at a point. 4 of them are 31°, 22°, 61°, 65°. What is the last one, in degrees?
3
5 angles meet at a point. 4 of them are 36°, 28°, 57°, 79°. What is the last one, in degrees?
4
5 angles meet at a point. 4 of them are 29°, 70°, 40°, 97°. What is the last one, in degrees?
5
5 angles meet at a point. 4 of them are 58°, 51°, 28°, 94°. What is the last one, in degrees?
6
5 angles meet at a point. 4 of them are 40°, 36°, 71°, 83°. What is the last one, in degrees?
7
5 angles meet at a point. 4 of them are 62°, 69°, 42°, 58°. What is the last one, in degrees?
8
5 angles meet at a point. 4 of them are 53°, 21°, 58°, 45°. What is the last one, in degrees?
9
5 angles meet at a point. 4 of them are 65°, 27°, 52°, 95°. What is the last one, in degrees?
10
5 angles meet at a point. 4 of them are 44°, 23°, 86°, 51°. What is the last one, in degrees?
11
5 angles meet at a point. 4 of them are 68°, 62°, 20°, 26°. What is the last one, in degrees?
12
5 angles meet at a point. 4 of them are 46°, 31°, 37°, 24°. What is the last one, in degrees?
13
5 angles meet at a point. 4 of them are 37°, 67°, 45°, 66°. What is the last one, in degrees?
14
5 angles meet at a point. 4 of them are 59°, 67°, 30°, 44°. What is the last one, in degrees?
15
5 angles meet at a point. 4 of them are 20°, 23°, 20°, 83°. What is the last one, in degrees?
16
5 angles meet at a point. 4 of them are 63°, 35°, 73°, 69°. What is the last one, in degrees?
17
5 angles meet at a point. 4 of them are 56°, 38°, 81°, 36°. What is the last one, in degrees?
18
5 angles meet at a point. 4 of them are 41°, 40°, 25°, 111°. What is the last one, in degrees?
19
5 angles meet at a point. 4 of them are 43°, 21°, 43°, 34°. What is the last one, in degrees?
20
5 angles meet at a point. 4 of them are 42°, 64°, 44°, 43°. What is the last one, in degrees?

What is in this set

The numbers in this set run from 4 to 112.
Every problem in it will meet at a point, so they add to 360°.
A careful solution takes 2 written steps on average.
The mistake this set invites most often, in 20% of the problems: angles round a whole point add to 360°, not 180° — 180° is a straight line.
Answers are a whole number.

Drawing 240 problems from this page produced 240 different ones, 100% — so a sheet of 20 is a new sheet almost every time.

The same skill, harder or easier

We would put this in front of a grade 6 class. That is our judgement, not a standard, and it is printed here so you can disagree with it. Everything else we put in that year.