Exercise 10B
Question 1
Name the interior opposite angles in the figure associated with the exterior angle.
(a) ACS
Sol : ∠ABC ,∠BAC
(b) RBA
Sol : ∠BAC, ∠ACB
(c) TAB
Sol : ∠ABC, ∠ACB
(d) QBC
Sol : ∠BAC, ∠ACB
(e) PAC
Sol : ∠ABC, ∠ACB
(f) BCU
Sol : ∠ABC, ∠BAC
Question 2
Find the unknown marked angle.
(a)
a=67°+38°=105° [ext. ∠property of a Δ]
(b)
119°=46°+b [ext. ∠property of a Δ]
b=119°-46°=73°
(c)
125°=59°+c [ext. ∠property of a Δ]
c=125°-59°=66°
(d)
88°=24°+a [ext. ∠property of a Δ]
a=88°-24°=64°
Question 3
Find ∠R
Fig to be added
(5x-2)°+(4x+15)° [ext. ∠property of a Δ]
5x-2°+4x+15°=130°
9x+13°=130°
9x=130°-13°=117°
$x=\frac{117}{9}$
∴x=13°
∠R=(4x+15)°
={(4×13)+15}°
={52+15)°=67°
Question 4
Find ∠ACD
Fig to be added
(7x-9)°=90°+(3x+5)°
7x-9-3x-5=90°
4x-14=90°
4x=90°-14°=104°
$x=\frac{104}{4}$
x=26°
∴∠ACD=(7x-9)°
={(7×26)-9}°
={182-9}°=173°
Question 5
Find the unknown marked angles, without using the angle sum property of a triangle
(a) Fig to be added
a=62°+32°=94° [ext. ∠property of a Δ]
b=180°-94°=86°
c=32°+86°=118° [ext. ∠property of a Δ]
(b) Fig to be added
q=180°-133°=47°
r=180°-90°=90°
(c) Fig to be added
x=180°-(65°+48°)
=180°-113°=67°
v=67° (corresponding ∠s AB||CD)
u=67°+65°=132° [ext. ∠property of a Δ]
(d) Fig to be added
y=50° (corresponding ∠s, AB||DE)∴x=25°+50°=75° [ext ∠s property of a Δ]
Question 6
Find x, without using the property of angle sum property of a triangle. State your reasons clearly
(a) Fig to be added
y=5x (corresponding ∠s, AB||DE)
4x+5x=72° [ext ∠s property of a Δ]
9x=72°
$x=\frac{72}{9}$
x=8°
(b) Fig to be added
∠ACD=180°-4x$x=\frac{180}{9}$
x=20°
(c) Fig to be added
(d) Fig to be added
5x=90°
$x=\frac{90}{5}$
x=18°
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