Geometry Practice Test 3

Question : 30 of 40

Marks: +1, -0

The smallest angle of a triangle is equal to two-thirds the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3 : 4 : 5 : 6. The largest angle of the triangle is twice its smallest angle. What is the sum of the second largest angle of the triangle and the largest angle of the quadrilateral?

160°
180°
190°
170°

Validate

Solution:

According to the statement the smallest angle of triangle =

2/3

of the smallest angle of the quadrilateral.
∠A =

2/3 × 3x

= 2x
Largest angle = 2 (smallest angle of the triangle)

∠B = 2(2x)
∠B = 4x

Now ∠C = 180° − (2x + 4x)
∠C = 180° − 6x
Sum of the second largest angle of the triangle + largest angle of the quadrilateral
= 180° − 6x + 6x
= 180°

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