计算： $(1)153^{\circ}29'42{'}{'}+26^{\circ}40'32{'}{'}=$$°$${'}$${'}{'}.(2)110^{\circ}36'-90^{\circ}37'28{'}{'}=$$°$${'}$${'}{'}.(3)62^{\circ}24'17{'}{'}\times 4=$$°$${'}$${'}{'}.(4)102^{\circ}43'21{'}{'}\div 3=$$°$${'}$${'}{'}.$

1. 计算秒相加并向分进位

$42'' + 32'' = 74'' = 1'14''$

2. 计算分相加并向度进位

$29' + 40' + 1' = 70' = 1^{\circ}10'$

3. 计算度相加得出最终结果

$153^{\circ} + 26^{\circ} + 1^{\circ} = 180^{\circ}$
所以，$153^{\circ}29'42'' + 26^{\circ}40'32'' = 180^{\circ}10'14''$

1. 将原角进行借位改写，以便进行减法

由于被减数中没有秒，且分的数值较小，需要借位：
$110^{\circ}36' = 110^{\circ}35'60'' = 109^{\circ}95'60''$

2. 度、分、秒分别对应相减

秒：$60'' - 28'' = 32''$
分：$95' - 37' = 58'$
度：$109^{\circ} - 90^{\circ} = 19^{\circ}$
所以，$110^{\circ}36' - 90^{\circ}37'28'' = 19^{\circ}58'32''$

1. 将度、分、秒分别乘以 4

$62^{\circ} \times 4 = 248^{\circ}$
$24' \times 4 = 96'$
$17'' \times 4 = 68''$

2. 对乘积进行进位化简

由于 $68'' = 1'8''$，则分变为 $96' + 1' = 97'$；
又由于 $97' = 1^{\circ}37'$，则度变为 $248^{\circ} + 1^{\circ} = 249^{\circ}$.
所以，$62^{\circ}24'17'' \times 4 = 249^{\circ}37'8''$

1. 先计算度除以 3

$102^{\circ} \div 3 = 34^{\circ}$

2. 计算分除以 3 并求出余数

$43' \div 3 = 14' \cdots\cdots 1'$

3. 将分的余数化为秒，与原秒相加后再除以 3

余数 $1' = 60''$，加上原有的 $21''$ 得 $81''$
$81'' \div 3 = 27''$
所以，$102^{\circ}43'21'' \div 3 = 34^{\circ}14'27''$