Question

In the below figure, if y is five times x, find the value of z.​

Answer 1

The value of z is 160°

Step-by-step explanation:

It has been given that

y = 5x

Sum of interior angles of a triangle is 180°. Thus, we have the equation

60° + x + y = 180°

Substitute, y = 5x

60° + x + 5x = 180°

Solve the equation for x

6x = 180 -60

6x = 120

x = 20°

Now, angle on a straight line adds to 180°

z + x = 180°

z + 20° = 180°

z = 180 - 20

z = 160°

#Learn More:

In triangle ABC, angle A = angle C and angle B = angle A + angle C. find the measures of the angles of the triangle.

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Answer 2

Answer:

$\red { Value \:of \:z } \green {= 60\degree }$

Step-by-step explanation:

$Given , \angle R = 60\degree$

$y = 5x \: --(1)$

$z + x = 180\degree \: ( Linear \:pair )$

$z = 180 - x \: ---(2)$

$z = \angle R + y$

$\pink { (Exterior \: angle \: z = Sum \: of }$

$\pink { interior\: opposite\: angles )}$

$\implies z = 60\degree + 5x \: [ From \:(1)]$

$\implies 180 - x = 60 + 5x \:[From \:(2) ]$

$\implies 180 - 60 = 5x + x$

$\implies 120 = 6x$

$\implies \frac{120}{6} = x$

$\implies x = 20$

/* Put x = 20 in equation (2) , we get

$Value \: of \: z = 180 - 20 = 160 \degree$

Therefore.,

$\red { Value \:of \:z } \green {= 60\degree }$

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