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Answers
Step-by-step explanation:
1) if AB=AC
then angle B = angle C
so let angle B and angle C = X
so. angle A + angle B + angle C = 180 ( sum of all side side triangle)
80 + X + X = 180
2X= 180-80
2X= 100
X= 100/2
X= 50
therefore. angle B is 50 degrees
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2) if PQ=QR
then angle P= angle R
so let angle P and angle R = X
so. angle P + angle Q + angle R = 180 ( sum of all side side triangle)
60 + X + X = 180
2X= 180-60
2X= 120
X=120/2
X= 60
therefore. angle R is 60 degrees
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3) angle K= 60
angle L = 40
exterior angle is equal to opposite of corresponding angle
therefore
exterior angle M = angle L + angle K
exterior angle M = 60+40
exterior angle M= 100 degrees
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4) exterior angle R= 130
angle Q = 70
exterior angle is equal to opposite of corresponding angle
therefore
exterior angle R= angle P + angle Q
130 = angle P + 70
angle P = 60
exterior angle P= 60 degrees
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5).
sum of all three angles of a triangle is always 180 degrees
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6) Pythagorean triplet = 2,3,4
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7). hypotenuse = 5 cm
base = 3 cm
perpendicular = ?
so according to the Pythagores theorem
(hypotenuse) ² = (base)² + (perpendicular )²
putting the value and take perpendicular as X
(5)² = (3)² + (X)²
25 - 9 = X²
X²= 16
X = √16
X=4
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8). let take equal sides as X
hypotenuse = √800 cm
base = X cm
perpendicular = X cm
so according to the Pythagores theorem
(hypotenuse) ² = (base)² + (perpendicular )²
800 = 2X²
400= X²
X = √200
X = 20