## The second angel of a triangle is 35 more than the first angle. The third angel is three times the first. Find the three angles

Question

The second angel of a triangle is 35 more than the first angle. The third angel is three times the first. Find the three angles

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1 week 2021-10-06T09:28:42+00:00 2 Answers 0

First angle =29

Second angle = 64

Third angle = 87

Step-by-step explanation:

First, we need to interpret this statement and write the mathematical form of the statement.

Let x, y, z equal to the first, second and third angle respectively.

The question says ‘The second angle of a triangle is 35 more than the first angle’

This implies y = 35 + x

‘The third angle is three times the first’, this implies z =3x

Now, the sum of angles in a triangle is equal to 180°

This implies

x + y + z = 180° ——————-(1)

But y = 35 +x and z =3x

substituting y =35 and z=3x in equation (1), our equation becomes;

x + 35 + x + 3x  = 180

we can rearrange this equation

x + 3x + x+ 35 = 180

5x + 35 = 180

subtract 35 from both-side of the equation

5x + 35 – 35 = 180 -35

5x = 145

Divide both-side by 5 to get the value  of x

5x/5 = 145/5

x = 29

To find the value of z, recall that z = 3x

substitute x = 29 into z =3x  thus;

z = 3(29)

z=87

but y= 35 + x

y = 35 + 29

y =64

x= 29, y =64   and z = 87

Therefore the first angle of the triangle  is 29, the second angle of the triangle  is 64 and the third angle of the triangle is 87

the first angle: 29

the second angle: 64

the third angle: 87

Step-by-step explanation:

the first angle: x

the second angle:  x + 35

the third angle: 3x

the sum of all three angle is 180

we have the equation: x + (x+35) + 3x =180

5x+35=180

5x = 145

x = 29