问题1：写以下每个角度的赞美词：
(i)20度
(ii)35°
(iii)90°
(iv)77度
(v)30°
解决方案：
(i) Given an angle 20°
As we Studied in this Chapter, the sum of angle and its compliment is 90
Therefore, its compliment will be (90° – 20° = 70°)
(ii) Given an angle 35°
As we Studied in this Chapter, the sum of angle and its compliment is 90
Therefore, its compliment will be (90° – 35° = 55°)
(iii) Given an angle 90°
As we Studied in this Chapter, the sum of angle and its compliment is 90
Therefore, its compliment will be (90° – 90° = 0°)
(iv) Given an angle 77°
As we Studied in this Chapter, the sum of angle and its compliment is 90
Therefore, its compliment will be (90° – 77° = 33°)
(v) Given an angle 30°
As we Studied in this Chapter, the sum of angle and its compliment is 90
Therefore, its compliment will be (90° – 30° = 70°)
问题2：写下以下每个角度的补充：
(i)54度
(ii)132度
(iii)138度
解决方案：
Since, Supplement = 2 × (Complement)
Supplement = 2 × (90°)
Therefore, Supplement = 180°
(i) Given an angle 54°
As we have Studied, the sum of angle and its Supplement is 180°
Therefore, Supplement of angle 54° will be (180° – 54° = 126°)
(ii) Given an angle 132°
As we have Studied, the sum of angle and its Supplement is 180°
Therefore, Supplement of angle 132° will be (180° – 132° = 48°)
(iii) Given an angle 138°
As we have Studied, the sum of angle and its Supplement is 180°
Therefore, Supplement of angle 54° will be (180° – 138° = 42°)
问题3：如果一个角度比其补角小28°，找到它的尺寸了吗?
解决方案：
Let the measure of the angle be ‘x’ degrees
As we studied Compliment = 90°
Thus, its Compliment will be (90 – x)°
Now,
The required angle = Complement of x – 28;
Therefore, our equation will become :
x = (90 – x) – 28
Now, after shifting x to left side, our equation will become:
2x = 62
x = 31
Therefore, the measure of the required angle will be 31°
问题4：如果某个角度大于其补角的一半30°，那么找到该角度的量度了吗?
解决方案：
Let the measure of the angle be ‘x’ degrees
As we studied Compliment = 90°
Thus, its Compliment will be (90 – x)°
Now,
The required angle = 30° + (Complement)/2 ;
Therefore, our equation will become :
x = 30° + (90 – x)° / 2
Now we will shift x to left side so 90 is also divided by 2 then our equation will become :
x + x/2 = 30° + 45°
3x/2 = 75°
x = 50°
Therefore, the measure of the required angle will be 50°
问题5：两个补充角之比为4：5。找到角度?
解决方案：
As given in the question Two Supplementary angles are in ratio 4 : 5
Assume, the angles are 4x and 5x (in degrees)
As we know both are supplementary angles,
Therefore, our equation will become 4x + 5x = 180°
9x = 180°
x = 20°
Now we put the value of x in both the angles i.e 4x and 5x
4x = 4 × (20°) = 80°
5x = 5 × (20°) = 100°
Hence, the required angles are 80° and 100°
问题6：两个补充角相差48°。找到角度?
解决方案：
As given in the question itself Two Supplementary angle differ by 48°
Consider x be one angle then its Supplementary angle will be equal to (180 – x)°
So, According to the question:
(180 – x) – x = 48
Now Shifting x to right side and 48 to left side then we get
(180 – 48) = 2x
2x = 132
x = 132 / 2
x = 66°
Now we find the second angle by putting the value of x i.e (180 – x)
Therefore, the second angle = 180 – 66 = 114°
Hence, the two angles are 66° and 114°
问题7：角度等于其补角的8倍。确定其措施?
解决方案：
According to the question, Required Angle = 8 times of its Complement
Let’s take x be one angle , then its Complementary angle will be (90 – x)
Now, as the question say our equation will become
x = 8 times of its complement
x = 8 (90 – x)
x = 720 – 8x
Now shifting 8x to left side we get,
x + 8x = 720
9x = 720
x = 80
Hence, the Required Angle is 80°