Question

8. If the degree measure of the angles of the quadrilateral are 4x, 7x, 9x and 10x, which is the
sum of the measures of the smallest angle and largest angle?
a) 140°
b) 150°
c) 168°
d) 180°
​

Answer 1

Answer:

C) 168 degree

Step-by-step explanation:

4x+7x+9x+10x=360

30x=360

x=12

substitute

4 x 12= 48

7 x 12 = 84

9 x 12= 108

10× 12 = 120

smallest angle + largest angle1

48+120

168 degree

Thanks

Answer 2

Given: Degree measure of the angles of a quadrilateral are $4x, 7x, 9x$ and $10x$

To find: The sum of measures of smallest and largest angle

Solution: According to the given question,

The four interior angles of the quadrilateral are $4x, 7x, 9x$ and $10x$

∵ Sum of interior angles of a quadrilateral = 360°

∴ $4x + 7x + 9x + 10x = 360$

⇒ $30x = 360$

⇒ $x = \frac{360}{30} = 12$

Now, the smallest angle is $4x$ and the largest angle is $10x.$

$4x =$ 4 × 12 = 48°

$10x$ = 10 × 12 = 120°

Sum of these two angles = 48 + 120 = 168°

Hence, the sum of the measures of the smallest angle and the largest angle is 168°.