Lines And Angles Test

Result

Lines And Angles Test - 3

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Weekly Quiz Competition

Question 1
1 / -0

The difference between the first and second angles of a triangle is 30°. The first angle measures 20° less than the sum of the other two. What kind of triangle is this?

A
Scalene triangle

B
Obtuse-angled triangle

C
Isosceles triangle

D
Equilateral triangle

Solution

Let the first, second and third angles of the triangle be x, y and z, respectively,
According to the given instructions,

x - y = 30° ... (i)
x = (y + z) - 20°
x - y = z - 20°

30° = z - 20° (From (i))
z = 50°

According to the angle sum property of triangle,
x + y + z = 180°
x + y + 50° = 180°

x + y = 130° ... (ii)
Solving (i) and (ii),

2x = 160°
x = 80°

Putting this value in (i),
80° - y = 30°

y = 80° - 30° = 50°
So, x = 80°, y = 50°, z = 50°

Since two angles of the triangle are equal, this is an isosceles triangle.
Question 2
1 / -0

Find the supplementary angle of the angle whose measure is 15^o more than the double of its supplementary angle.

A
55°

B
25°

C
35°

D
65°

Solution

Let the measure of the angle be x.

According to the given instructions,

x = 15°+ 2(180° - x) [∵ (180° - x) is the supplementary angle of x]
x = 15° + 360° - 2x

x = -2x + 375°
3x = 375°
x = 125°

Supplementary angle of x = 180°- x = 180° - 125° = 55°