The ratio of the angles of a triangle is 3 : 4 : 5. The three angles of a quadrilateral is equal to three angles of this triangle. What is the sum of the largest angle and second smallest angle of the quadrilateral ?
A) 225 deg
B) 210 deg
C) 205 deg
D) 245 deg
Answers
Answer:
The sum of the largest angle and second smallest angle of the quadrilateral is 240°
Step-by-step explanation:
Let the given angles of the triangle are 3a , 4a and 5a.
We know that the sum of all angles of triangle is 180°.
So, sum of 3a , 4a, and 5a = 180°
= > 3a + 4a + 5a = 180°
= > 12a = 180°
= > a = 180° / 12
= > a = 15°
Now,
angles of the given triangle are 3a = 3( 15° ) = 45° , 4a = 4 ( 15° ) = 60° and 5( 15° ) = 75°
The angles of the triangle which are given in the ratio are 45° , 60° and 75°.
It is given that the three angles of a quadrilateral are equal to the given angles of the triangle.
So, three angles of the quadrilateral are 45° , 60° and 75°.
From the properties of quadrilaterals, we know that the sum of all angles of a quadrilateral is 360°.
Now, let the fourth angle of the quadrilateral is k,
So, sum of 45° , 60° , 70° and k should be 360°.
= > 45° + 60° + 70° + k = 360°
= > 180° + k = 360°
= > k = 360° - 180°
= > k = 180°
Then,
angles of the quadrilateral are : 45° , 60° ,75° and 180°.
Among the angles of the quadrilateral, 180° is the largest angle and 60° is the second largest angle.
Sum of the largest and second smallest angle = 180° + 60° = 240°