State the test and the correspondence of vertices by which the
given triangles in the figure are congruent.
Answers
Answer:
Step-by-step explanation:
\underline{\underline{\maltese\: \: \textbf{\textsf{Question}}}}
✠Question
The four angle of a quadrilateral are x°, (x - 10)°, (x + 30)° and 2x°. Find all the angles of quadrilateral and also write the greatest angle.
\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}
✠Answer
Our required angles are 68°, 58°, 98°, and 136°. And the greatest angles is 136°.
\underline{\underline{\maltese\: \: \textbf{\textsf{Given}}}}
✠Given
The four angle of a quadrilateral are x°, (x - 10)°, (x + 30)° and 2x°.
\underline{\underline{\maltese\: \: \textbf{\textsf{To\ Find}}}}
✠To Find
We have to find out all the angles of quadilateral. Also, we have to write the greatest angle.
\underline{\underline{\maltese\: \: \textbf{\textsf{Basic\ Terms}}}}
✠Basic Terms
Quadrilateral : A quadrilateral is a polygon in Euclidean plane geometry with four edges and four vertices.
Angle : An angle is a combination of two rays (half-lines) with a common endpoint.
\underline{\underline{\maltese\: \: \textbf{\textsf{Solution}}}}
✠Solution
As per the given information, we know that the known values are the measure of all the four angles of quadilateral.
Then firstly, by using the angles sum property of quadilateral we will find out the value of x.
After, that by applying the value of x in the given angles we will find out the angles of quadilateral.
\underline{\underline{\maltese\: \: \textbf{\textsf{Calculations}}}}
✠Calculations
We know that :-
{\underline{\boxed{\sf {Sum\ of\ all\ angles\ of\ quadilateral\ =\ 360^{\circ}.}}}}
Sum of all angles of quadilateral = 360
∘
.
By applying the values, we get :-
\sf \mapsto {x\ +\ (x\ -\ 10)^{\circ}\ +\ (x\ +\ 30)^{\circ}\ +\ 2x\ =\ 360^{\circ}}↦x + (x − 10)
∘
+ (x + 30)
∘
+ 2x = 360
∘
\sf \mapsto {x\ +\ x\ +\ x\ +\ 2x\ -\ 10\ +\ 30\ =\ 360^{\circ}}↦x + x + x + 2x − 10 + 30 = 360
∘
\sf \mapsto {3x\ +\ 2x\ -\ 10\ +\ 30\ =\ 360^{\circ}}↦3x + 2x − 10 + 30 = 360
∘
\sf \mapsto {5x\ +\ 20\ =\ 360^{\circ}}↦5x + 20 = 360
∘
\sf \mapsto {5x\ =\ 360^{\circ}\ -\ 20}↦5x = 360
∘
− 20
\sf \mapsto {5x\ =\ 340^{\circ}}↦5x = 340
∘
\sf \mapsto {x\ =\ \cancel \dfrac{340^{\circ}}{5}}↦x =
5
340
∘
{\therefore{\underline{\boxed{\tt {x\ =\ 68^{\circ}.}}}}}∴
x = 68
∘
.
Now, we have the value of x. So, now we will find out the angles of quadilateral and the greatest angle.
➊ 1st angle = x = 68°.
➋ 2nd angle = (x - 10)° = (68 - 10)° = 58°.
➌ 3rd angle = (x + 30)° = (68 + 30)° = 98°.
➍ 4th angle = 2x = 2(68)° = 136°.
{\therefore{\underline{\sf{\pmb{Hence,\ greatest\ angle\ of\ quadilateral\ =\ 136^{\circ}.}}}}}∴
Hence, greatest angle of quadilateral = 136
∘
.
Hence, greatest angle of quadilateral = 136
∘
.