Question

If the measure of the angles of a triangle are 4y, 54° and 42° what will be the value of y.​

Answer 1

Correct Question :-

• If the measure of the angles of a triangle are 4y, 54° and 42° what will be the value of y.

Options are :-

1. y = 21°
2. y = 12°
3. y = 33°
4. none

Answer :-

• Value of 'y' = 21° (Option A)

Given :-

• First angle of triangle = 4y°
• Second angle of triangle = 54°
• Third angle of triangle = 42°

To Find :-

• Value of 'y' = ?

Explanation :-

As above given, we have all 3 angles of the triangles and we have to find the value of 'y'. But first we need to understand a theorem.

Angle sum property of triangles -

• Angle sum property of triangle states that the sum of interior angles of a triangle is 180°

Now,  making an equation,

$\rm : \: \longrightarrow 4y^\circ + 54^\circ + 42^\circ = 180^\circ$

$\rm : \: \longrightarrow 4y^\circ + 96^\circ = 180^\circ$

$\rm : \: \longrightarrow 4y^\circ = 180^\circ - 96^\circ$

$\rm : \: \longrightarrow 4y^\circ = 84^\circ$

$\rm : \: \longrightarrow y^\circ = \dfrac{84^\circ}{4}$

$\blue { \boxed { \bf : \: \longrightarrow y = 21^\circ \qquad \star}}$

For Verification,

$\rm : \: \longrightarrow 4(21)^\circ + 54^\circ + 42^\circ = 180^\circ$

$\rm : \: \longrightarrow 84^\circ + 54^\circ + 42^\circ = 180^\circ$

$\rm : \: \longrightarrow 84^\circ + 96^\circ = 180^\circ$

$\rm : \: \longrightarrow 180^\circ = 180^\circ$

$\bf : \: \longrightarrow L.H.S = R.H.S$

$\rm \odot \: Hence \: Verified \: \: \: \; \checkmark$

Hence, the value of 'y' is 21°