您好，这10道题都是考核（非谓语动词）的用法，答案的解答如下：
1）The man (making) a phone call is the chairman of the committee.（题目拼错了）
主干结构是 the man .... is the chairman of the committee. make 和 the man 是主谓关系，所以使用（现在分词）的 -ing 结构，作后置定语修饰 the man；句子可以改写为 The man (who is) making a phone call is the chairman of the committee.
2）The stadium (designed) last year is the biggest one in our city.
主干结构是 The stadium .... is the biggest one in our city. design 和 the stadium 是（动宾关系），所以用（过去分词）的 -ed 结构，也就是被动语态的意思，作后置定语修饰 the stadium；句子可以改写为 The stadium (which was) designed last year is the biggest onein our city.
3）The man (standing) there is our teacher.
主干结构是 The man ... is our teacher. stand 和 the man 是主谓关系，所以使用（现在分词）的 -ing 结构，作后置定语修饰 the man；句子可以改写为 The man (who is) standing there is our teacher.
4）My brother is a lawyer (working) in a court.
主干结构是 My brother is a layer ....，my brother 和 work 是主谓关系，所以用（现在分词）的 -ing 结构，作后置定语修饰 lawyer；句子可以改写为 My brother is a lawyer (who) works in a court.
5）The building (being built) now will be finished in two months. 句子有明确的时间状语 now，和一般将来时的被动语态，表示 building 正在被建造中，所以是（进行式），而 building 和 build 是动宾关系，也就是被动语态的意思，作后置定语修饰 the building，句子可以改写为 The building (which is) being built now will be finished in two months.
6）He often carefully watches the doctors in the (operating) room.
这里的考核是（分词）作（定语），operating room 是（手术室）的英语，用（现在分词）-ing 形式；
7）The (sleeping) baby is my sister's son.
这里的考核是（分词）作（定语），句子可以改写为，The baby (who is sleeping) is my sister's son. 所以 sleep 和 baby 是（主谓关系），the baby who is sleeping = a sleeping baby，所以用（现在分词）-ing 形式，作（定语）修饰 baby；
8）Today there are more airplanes (carrying) more people than ever before in the skies.
主干是 Today there are more airplanes ....，airplanes 和 carry 是（主谓关系），故用（现在分词）-ing 形式，句子可以改写为 .... the airplanes that carry more ....，作后置定语修饰 airplanes；
9）The woman (washing) dishes over there is my aunt.
主干是 The woman is my aunt. 理由和第1题和第3题雷同；
10）The question (being discussed) at present has something important to do with our daily life.
主干是 The question .... has something important to do ....；理由和第5题雷同，表示 the question 是（正在进行中），有时间状语 at present。
希望这样的解析可以帮到您。
1.making
2.designed
3.standing
4.working
5.being built
6.operating
7.sleeping
8.carrying
9.washing
10.being discussed
正在打电话的人是委员会主席。
2.designed
去年设计的体育场是该市最大的体育场。
3.standing
那个站在那儿的人是我们的老师。
4.working
我哥哥是一名在法院工作的律师。
5.being built
这幢大楼将在两个月后完工。
6.operating
他经常仔细观察手术室里的医生。
7.sleeping
正在睡觉的婴儿是我姐姐的儿子。
8.carrying
今天，天空中有比以往任何时候都多的飞机载着更多的人。
9.washing
那个正在洗碗的女人是我的阿姨。
10.being discussed
目前正在讨论的问题与我们的日常生活有重要关系。本回答被提问者采纳