Question

Three angles of a quadrilateral are equal and the fourth angle measures 75 degree. What is the measure of each equal angles .
(With steps)

​

Answer 1

$❒ \: \: { \underline{ \underline{ \textbf{\textsf{{ \: \: Given \: : \:}{}}}}}}$

Three angles of a quadrilateral are equal and the fourth angle measures 75°

$❒ \: \: { \underline{ \underline{ \textbf{\textsf{{ To Find \: : \:}{}}}}}}$

The measure of each equal angles

$❒ \: \: { \underline{ \underline{ \textbf{\textsf{{ Solution \::}{}}}}}}$

Let's assume the three angles of the quadrilateral as x.

As, we all know,

Sum of the angles of a quadilateral = 360°

$\therefore \: \: \: \tt \: x + x + x + 75 {}^{ \circ} = 360 {}^{ \circ}\\ \\ \\ ⇢ \: \: \: \: \: \: \: \: \tt \: 3x + 75 {}^{ \circ} = 360 {}^{ \circ} \: \: \: \\ \\ \\ \tt \:⇢ \: \: \: \: \: \: \: \: \tt \: 3x = \: 360 {}^{ \circ} - 75 {}^{ \circ} \\ \\ \\ ⇢ \: \: \: \: \: \: \: \: \tt \: 3x = 285 {}^{ \circ} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ ⇢ \: \: \: \: \: \: \: \: \tt \: x \: \: = \: \: \frac{285{}^{ \circ}}{3} \: \: \: \: \: \: \: \\ \\ \\ \tt \: ⇢ \: \: \: \: \: \: \: \: \tt \: \boxed{ \pmb{ \mathfrak { \purple{x \: \: = \: \: \: \: 95 {}^{ \circ}}}}} \: \bigstar \:$

Hence,

$\\ \circ \: { \textbf{ \textsf{ 1st angle}}} = { \pmb{ \mathfrak { \bold{ 95 ^{ \circ}}}}}$

$\\ \circ \: { \textbf{ \textsf{2nd angle}}} = { \pmb{ \mathfrak { \bold{ 95 ^{ \circ}}}}}$

$\\ \circ \: { \textbf{ \textsf{3rd angle}}} = { \pmb{ \mathfrak { \bold{ 95 ^{ \circ}}}}}$

$\\ \circ \: { \textbf{ \textsf{4th angle}}} = { \pmb{ \mathfrak { \bold{ 75 ^{ \circ}}}}}$

________________________________________

$❒ \: \: { \underline{ \underline{ \textbf{\textsf{{ Verification \::}{}}}}}}$

$\\ { \pmb{ \textsf{★ Sum of all the angles of the quadrilateral = 360°}}}$

$⇢ \: \: \: \: \: \tt \: x + x + x + 75 {}^{ \circ} = 360 {}^{ \circ}$

Substituting the value of x :

$\\ ⇢ \: \tt \: 95 {}^{ \circ} + 95 {}^{ \circ} + 95 {}^{ \circ} + 75 {}^{ \circ} = 360 {}^{ \circ} \\ \\ \\ ⇢ \: \: \: \tt \: 360 {}^{ \circ} = 360 {}^{ \circ} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \therefore \: \: \purple{ \pmb{\textbf{L.H.S = R.H.S}}}$

@MrCyber

Answer 2

Answer:

❒ \: \: { \underline{ \underline{ \textbf{\textsf{{ \: \: Given \: : \:}{}}}}}}❒

Given :

Three angles of a quadrilateral are equal and the fourth angle measures 75°

❒ \: \: { \underline{ \underline{ \textbf{\textsf{{ To Find \: : \:}{}}}}}}❒

To Find :

The measure of each equal angles

❒ \: \: { \underline{ \underline{ \textbf{\textsf{{ Solution \::}{}}}}}}❒

Solution :

Let's assume the three angles of the quadrilateral as x.

As, we all know,

Sum of the angles of a quadilateral = 360°

\begin{gathered} \therefore \: \: \: \tt \: x + x + x + 75 {}^{ \circ} = 360 {}^{ \circ}\\ \\ \\ ⇢ \: \: \: \: \: \: \: \: \tt \: 3x + 75 {}^{ \circ} = 360 {}^{ \circ} \: \: \: \\ \\ \\ \tt \:⇢ \: \: \: \: \: \: \: \: \tt \: 3x = \: 360 {}^{ \circ} - 75 {}^{ \circ} \\ \\ \\ ⇢ \: \: \: \: \: \: \: \: \tt \: 3x = 285 {}^{ \circ} \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ ⇢ \: \: \: \: \: \: \: \: \tt \: x \: \: = \: \: \frac{285{}^{ \circ}}{3} \: \: \: \: \: \: \: \\ \\ \\ \tt \: ⇢ \: \: \: \: \: \: \: \: \tt \: \boxed{ \pmb{ \mathfrak { \purple{x \: \: = \: \: \: \: 95 {}^{ \circ}}}}} \: \bigstar \: \\ \\ \\ \end{gathered}

∴x+x+x+75

∘

=360

∘

⇢3x+75

∘

=360

∘

⇢3x=360

∘

−75

∘

⇢3x=285

∘

⇢x=

3

285

∘

⇢

x=95

∘

x=95

∘

★

Hence,

\begin{gathered} \\ \circ \: { \textbf{ \textsf{ 1st angle}}} = { \pmb{ \mathfrak { \bold{ 95 ^{ \circ}}}}} \\ \end{gathered}

∘ 1st angle=

95

∘

95

∘

\begin{gathered}\\ \circ \: { \textbf{ \textsf{2nd angle}}} = { \pmb{ \mathfrak { \bold{ 95 ^{ \circ}}}}} \\ \end{gathered}

∘ 2nd angle=

95

∘

95

∘

\begin{gathered}\\ \circ \: { \textbf{ \textsf{3rd angle}}} = { \pmb{ \mathfrak { \bold{ 95 ^{ \circ}}}}} \\ \end{gathered}

∘ 3rd angle=

95

∘

95

∘

\begin{gathered}\\ \circ \: { \textbf{ \textsf{4th angle}}} = { \pmb{ \mathfrak { \bold{ 75 ^{ \circ}}}}} \\ \end{gathered}

∘ 4th angle=

75

∘

75

∘

________________________________________

❒ \: \: { \underline{ \underline{ \textbf{\textsf{{ Verification \::}{}}}}}}❒

Verification :

\begin{gathered} \\ { \pmb{ \textsf{★ Sum of all the angles of the quadrilateral = 360°}}} \\ \end{gathered}

★ Sum of all the angles of the quadrilateral = 360°

★ Sum of all the angles of the quadrilateral = 360°

\begin{gathered}⇢ \: \: \: \: \: \tt \: x + x + x + 75 {}^{ \circ} = 360 {}^{ \circ} \\ \end{gathered}

⇢x+x+x+75

∘

=360

∘

Substituting the value of x :

\begin{gathered} \\ ⇢ \: \tt \: 95 {}^{ \circ} + 95 {}^{ \circ} + 95 {}^{ \circ} + 75 {}^{ \circ} = 360 {}^{ \circ} \\ \\ \\ ⇢ \: \: \: \tt \: 360 {}^{ \circ} = 360 {}^{ \circ} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \therefore \: \: \purple{ \pmb{\textbf{L.H.S = R.H.S}}} \\ \\ \end{gathered}

⇢95

∘

+95

∘

+95

∘

+75

∘

=360

∘

⇢360

∘

=360

∘

∴

L.H.S = R.H.S

L.H.S = R.H.S

\begin{gathered} \\ \end{gathered}