Question

6.one
angle of a triangle is 80 degree
and the other 2 angles are in
ratio 1:3. Find these
angles​

Answer 1

★ How to do :-

Here, we are given with the measurement of one of the angle of a triangle. We are also given with the ratio of other two angles of the same triangle. We are asked to find the value of these both angles. Here, we can make use of a concept that says that all the angles of a triangle always measures 180° when added together. We can also verify that whether the obtained answer is correct of not. We also use variables in this sum so that we can find the value of those and then find both angles. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \underline{\boxed{\sf Interior \: angle \: property = {180}^{\circ}}}}$

Substitute the given hints and values.

${\tt \leadsto 1 : 3 + {80} ^{\circ} = {150}^{\circ}}$

Insert a variable x to both part of ratio.

${\tt \leadsto 1x + 3x + 80 = 180}$

Add both the values having same variables.

${\tt \leadsto 4x + 80 = 180}$

Shift the number 80 from LHS to RHS, changing it's sign.

${\tt \leadsto 4x = 180 - 80}$

Subtract the values on RHS.

${\tt \leadsto 4x = 100}$

Shift the number 4 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{100}{4}}$

Simplify the fraction to get the value of x.

${\tt \leadsto x = \cancel \dfrac{100}{4} = 25}$

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Value of second angle :-

${\tt \leadsto 1x = 1 \times 25}$

${\tt \leadsto \pink{\underline{\boxed{\tt {25}^{\circ}}}}}$

Value of third angle :-

${\tt \leadsto 3x = 3 \times 25}$

${\tt \leadsto \pink{\underline{\boxed{\tt {75}^{\circ}}}}}$

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Verification :-

${\tt \leadsto \angle{1} + \angle{2} + \angle{3} = {180}^{\circ}}$

Substitute the values.

${\tt \leadsto {80}^{\circ} + {25}^{\circ} + {75}^{\circ} = {180}^{\circ}}$

Add all the values on LHS.

${\tt \leadsto {180}^{\circ} = {180}^{\circ}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!

Answer 2

Answer:

• 25°
• 75°

Step-by-step explanation:

Given

• One angle of a triangle = 80°
• Ratio of other two angles = 1 : 3

To find

• Measure of each angle

Solution

↪ Let the other two angles be 1x and 3x where x is any number.

↪ We know that sum of all the angles in a triangle is equal to 180° called as the angle sum property.

Hence we get,

• 1x + 3x + 80° = 180°
• 4x + 80° = 180°
• 4x = 100°
• x = 100/4
• x = 25°

Hence, the remaining two angles are,

• 1x = 25°
• 3x = 75°

Verification

• Sum of all angles is equal to 180°
• 25° + 75° + 80° = 180°
• 100° + 80° = 180°
• 180° = 180°
• L.H.S = R.H.S