心甘情願地做
把「心裡的高興」放在答應這件事上：因為心裡是願意的，所以回答得又快又乾脆。
r · B1
In a way that shows you are willing to do something and do not mind doing it at all. Nobody has to push you, and you often want to help.
樂意地
核心畫面
One way to hold gladly is as glad with a -ly stuck on the end: doing something with gladness inside you. Picture a person who is asked for help and whose face lights up before they answer. That one picture then leans two ways. It can point at the heart behind the answer — yes, and I don't mind at all. Or it can point at the face and the voice at the moment itself — the way a person sounds when good news has just landed.
gladly 可以想成 glad（高興）＋ -ly（……地）：帶著高興去做一件事。畫面是有人開口請你幫忙，你的表情先…更多收起
gladly 可以想成 glad（高興）＋ -ly（……地）：帶著高興去做一件事。畫面是有人開口請你幫忙，你的表情先亮起來，然後才回答。這個畫面可以往兩邊倒。一邊是那份心意——我願意，而且一點都不覺得麻煩。一邊是當下的樣子——好消息剛到，說話的語氣就是高興的。From the word’s history
From Old English glædlīċe, that is glad + -ly; compare Danish glædelig and Icelandic gleðilegur.
來自古英語 glædlīċe，也就是 glad 加上 -ly；丹麥語 glædelig、冰島語 gleðilegur 是同一條線上的字。所以這個字從一開始就是「帶著高興地」。
Wiktionary etymology supplied in this packet (kaikki:3f6f69a190036ae4:1023470904:17991)
Two branches
高興的樣子
同一份高興，這次不是放在決定上，而是露在臉上和聲音裡，變成別人看得到、聽得到的樣子。
r · B2
In a way that shows you are pleased or happy at that moment. It describes how someone speaks, looks, or acts when something good has just happened.
高興地