Correct

高兴 vs 快乐

/ gāoxìng vs kuàilè /
Strokes

Formula

1
快乐教育 (happy education)
2
快乐晚会 (happy party)
3
快乐时光 (happy time)

Definition

高兴 as an Adjective or Verb, 快乐 as an Adjective, which means [delighted; be pleased to; happy].

Example

高兴 is applied to mood, mostly sth. temporary, 快乐 is applied to sentiments that may be temporary or lasting. 快乐 also implies happiness and satisfaction and is more literary.
1) In examples ① and ②, it is about sth. temporary and it is colloquial., so 高兴 should be used.

2) In examples ③ and ④, what is referred to is not temporary and is more formal, with happiness implied, so 快乐 is used.

3) When referring to ordinary things, 高兴 or 快乐 either word can be used.

4) When referring to formal occasions, 快乐 and not 高兴 is used, e.g. 快乐教育 (happy education), 快乐晚会 (happy party), 快乐时光 (happy time), etc.
快乐教育 (happy education) 快乐晚会 (happy party) 快乐时光 (happy time)
1
Jīntiān
今天
néng
lái
kàn
  
,
zhēn
gāoxìng
高兴
  

I am very glad that you are able to see me today.

2
zhīdào
知道
wèishénme
为什么
  
,
hǎoxiàng
好像
yǒudiǎnr  
有点儿
gāoxìng
高兴
  

I don't know why he's a bit unhappy.

3
Zhù
shēng
生日
kuài
快乐
  
!

Happy birthday to you.

4
suīrán
虽然
huó
le
dào
liùshí
六十
suì
  
,
dànshì
但是
zǒngdeláishuō
总的来说
  
,
shì
kuài
快乐
de
shēng
一生
  

Though he died in his sixties, generally speaking, he's happy all his life.

5
Jīntiān
今天
dào
遇到
de
shì
  
,
dōu
shì
ràng
rén
tài
gāoxìng
高兴
  
(
kuài
快乐
  
)
de
shì
  

What we faced today is unpleasing.

高兴 is also a Verb, meaning to be delighted in doing sth. (usually concrete).
6
gāoxìng
高兴
chuān
穿
zhè
jiàn
fu
衣服
  
,
jiù
chuān
穿
zhè
jiàn
  

She like wearing this one, so put on it.

7
Zhì
至于
zhè
fēng
xìn
  
,
gāoxìng
高兴
zěnme
怎么
xiě
jiù
zěnme
怎么
xiě
  

He can write the letter at his will.

8
A
A
  
:
Zhè
jiàn
shì
zěnme
怎么
zhèyàng
这样
chǔ
处理
  
?
B
B
  
:
gāoxìng
高兴
zhème
这么
bàn
  
!

A: How can you deal with it this way? B: It's none of your business.

Related

快乐高兴