📌Answer to Question #1️⃣👆
✅️A triangle has angles in the ratio 2:3:5. What are the measures of the angles?
🔑To solve this question, we can set up an equation using the given ratio.
And, we know that the sum of the three angles of a triangle is 180°.
If we name the angles by the symbols: a, b and c. Then,
a + b + c = 180°
Given that
a/b=2/3 and b/c=3/5, we get
a= 2/3b and b= 3/5c, so,
a=2/3(3/5c)=2/5c.
Now, both a and b are expressed interms of c. So,
In the equation
a + b + c = 180°
Replace a and b to get,
2/5c + 3/5c + c = 180°
Which is one equation in one variable.
multiply both sides by 5 to get rid of the denominator :
2c + 3c + 5c = 5×180
10c =900
c = 90
Then, b= 3/5c
=> b = 3/5(90)
= 3×(90/5) = 3×18 = 54,
and
a = 2/3b = 2/3(54)= 36.
✅Check: 36 + 54 + 90 = 180.
📚OR🔑
Let x be the common multiplier for the ratio.
The measures of the angles can be represented as 2x, 3x, and 5x.
Since the sum of the angles in a triangle is 180 degrees, we can set up the equation:
2x + 3x + 5x = 180
Simplifying the equation:
10x = 180
Dividing both sides by 10:
x = 18
Now we can find the measures of the angles:
2x = 2 × 18 = 36 degrees
3x = 3 × 18 = 54 degrees
5x = 5 × 18 = 90 degrees
Therefore, the measures of the angles in the triangle are 36 degrees, 54 degrees, and 90 degrees.
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