Question

Four angles are in the ratio 2:3:4:11 The largest angle is 198 degrees show the four angles will fit together at a point with no gaps

Answer 1

Answer: The four angles will fit together at a point with no gaps.

Step-by-step explanation:

Given: The ratio of four angles 2:3:4:11.

Let the angles be 2x , 3x, 4x and 11x.

Larget angle= 11x

As per given,

$11x = 198\\\\\Rightarrow\ x=\dfrac{198}{11}\\\\\Rightarrow\ x=18^{\circ]$

Then, $2x= 2 \times 18^{\circ}=36^{\circ}$

$3x=3\times 18^{\circ}=54^{\circ}$

$4x= 4\times18^{\circ}=72^{\circ}$

All angles are : $36^{\circ},54^{\circ},72^{\circ},198^{\circ}$

Sum of all angles =  they $36^{\circ}+54^{\circ}+72^{\circ}+198^{\circ}=360^{\circ}\ \ \ \text{[Total angle at a point = }360^{\circ}]$

Hence, the four angles will fit together at a point with no gaps.