which of the following pair is supplementary angle 1)13,77 2)10,70 3)120,60 4)50,40
Answers
Answer:
120 and 60 is the correct pair because their sum is 180°
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Page No 26:
Question 1:
The measures of some angles are given below. Write the measures of their complementaryangles.
(i) 40° (ii) 63° (iii) 45°(iv) 55° (v) 20° (vi) 90° (vii) x°
ANSWER:
(i)
Let the measure of the complementary angle be a.
40 + a = 90
∴ a = 50°
Hence, the measure of the complement of an angle of measure 40° is 50°
(ii)
Let the measure of the complementary angle be a.
63 + a = 90
∴ a = 27°
Hence, the measure of the complement of an angle of measure 63° is 27°
(iii)
Let the measure of the complementary angle be a.
45 + a = 90
∴ a = 45°
Hence, the measure of the complement of an angle of measure 45° is 45°
(iv)
Let the measure of the complementary angle be a.
55 + a = 90
∴ a = 35°
Hence, the measure of the complement of an angle of measure 55° is 35°
(v)
Let the measure of the complementary angle be a.
20 + a = 90
∴ a = 70°
Hence, the measure of the complement of an angle of measure 20° is 70°
(vi)
Let the measure of the complementary angle be a.
90 + a = 90
∴ a = 0°
Hence, the measure of the complement of an angle of measure 00° is 0°
(vii)
Let the measure of the complementary angle be a.
x + a = 90
∴ a = (90 − x)°
Hence, the measure of the complement of an angle of measure x° is (90 − x)°
Page No 26:
Question 2:
(y − 20)° and (y + 30)° are the measures of complementary angles. Find the measure of each angle.
ANSWER:
Sum of two complementary angles is 90°
∴ (y − 20)° + (y + 30)° = 90°
⇒ y − 20 + y + 30 = 90
⇒ 2y + 10 = 90
⇒ 2y = 80
⇒ y = 40
Hence, the measure of the two angles are 20° and 70°.
Page No 27:
Question 1:
Write the measures of the supplements of the angles given below.
(i) 15° (ii) 85° (iii) 120° (iv) 37° (v) 108° (vi) 0° (vii) a°
ANSWER:
(i)
Let the measure of the supplementary angle be a.
15 + a = 180
∴ a = 165°
Hence, the measure of the supplement of an angle of measure 15° is 165°.
(ii)
Let the measure of the supplementary angle be a.
85 + a = 180
∴ a = 95°
Hence, the measure of the supplement of an angle of measure 85° is 95°.
(iii)
Let the measure of the supplementary angle be a.
120 + a = 180
∴ a = 60°
Hence, the measure of the supplement of an angle of measure 120° is 60°.
(iv)
Let the measure of the supplementary angle be a.
37 + a = 180
∴ a = 143°
Hence, the measure of the supplement of an angle of measure 37° is 143°.
(v)
Let the measure of the supplementary angle be a.
108 + a = 180
∴ a = 72°
Hence, the measure of the supplement of an angle of measure 108° is 72°.
(vi)
Let the measure of the supplementary angle be a.
0 + a = 180
∴ a = 180°
Hence, the measure of the supplement of an angle of measure 0° is 180°.
(vii)
Let the measure of the supplementary angle be x.
a + x = 180
∴ x = (180 − a)°
Hence, the measure of the supplement of an angle of measure a° is (180 − a)°.
Page No 27: