Question

11. If the measure of the angles of a triangle are 4y. 54 and 42(in degrees ). what will be the value of
(1 Point)
y= 21 degree
y=12 degree
none​

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 :-

• y = 21°
• y = 12°
• none

Answer ::

[ Option a. y = 21 ] is the correct option.

Step-by-step explanation ::

To Find:-

• The value of y

Solution:-

Given that,

• The measure of the angles of a triangle is 4y, 54° and 42°

ACCORDING THE QUESTION,

As we know that,

1st angle + 2nd angle + 3rd angle = 180° [ angle sum property of triangle ]

➦ 4y + 54° + 42° = 180°

➦ 4y + 54 + 42 = 180

➦ 4y + 96 = 180

➦ 4y = 180 - 96

➦ 4y = 84

➦ y = 84 / 4

➦ y = 21

The value of y is 21.

Now Verification,

➦ 4y + 54 + 42 = 180

➦ 4*21 + 54 + 42 = 180

➦ 84 + 54 + 42 = 180

➦ 84 + 96 = 180

➦ 180 = 180

L.H.S = R.H.S

HENCE, VERIFIED !

Answer 2

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°