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Mathematics

Grade-8

Easy

Question

Find the measure of all the angles.

$∠ a = 120 °, ∠ b = 20 °, ∠ c = 40 °, ∠ d = 120 °, ∠ e = 40 °$
$∠ a = 100 °, ∠ b = 40 °, ∠ c = 120 °, ∠ d = 40 °, ∠ e = 40 °$
$∠ a = 100 °, ∠ b = 40 °, ∠ c = 140 °, ∠ d = 20 °, ∠ e = 20 °$
$∠ a = 120 °, ∠ b = 60 °, ∠ c = 100 °, ∠ d = 20 °, ∠ e = 20 °$

hint Hint:

In the triangle ABC,AB=AC
Angles opposite to equal sides are equal.

The correct answer is: $angle a equals 100 degree comma angle b equals 40 degree comma angle c equals 140 degree comma angle d equals 20 degree comma angle e equals 20 degree$

In the triangle ABC,AB=AC
Angles opposite to equal sides are equal.
So, angle b=40
and Then in the triangle ABC , the sum of the angles are 180
angle a + angle b + 40=180
angle a+40+40 =180
angle a+80=180
angle a=180-80
angle a= 100
WE know that angle b and angle c form a linear pair
So, they are supplementary
angle b +angle c=180
40+angle c=180
angle c=180-40
angle c=140
given that AB=BD
We know that angles opposite to equal sides are equal.
angle d= angle e
now, angle b is the exterior angle of triangle ABD
So, angle b=Angle d + angle e
40=2*angle d
angle d= 40/2
angle d=20
and angle e=20
$angle a equals 100 degree comma angle b equals 40 degree comma angle c equals 140 degree comma angle d equals 20 degree comma angle e equals 20 degree$

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