Mathematics
If one angle of a parallelogram is 30° less than twice the smallest angle, then measure of each angle will be :
60°, 80°, 80°, 140°
70°, 110°, 70°, 110°
60°, 120°, 60°, 120°
75°, 105°, 75°, 105°
Answer
Let the smallest angle of the parallelogram be denoted as x.
Given,
One angle of a parallelogram is 30° less than twice the smallest angle = 2x - 30°.
In a parallelogram, consecutive angles are supplementary and opposite angles are equal.
x + 2x - 30° = 180°
3x - 30° = 180°
3x = 180° + 30°
3x = 210°
x = 70°.
The two smaller angles are both 70°.
The two larger angles are both 2(70°) - 30° = 110°.
Hence, option 2 is the correct option.
Related Questions
ABCD is a parallelogram in which ∠A = 72°. Measures of ∠B, ∠C and ∠D respectively will be :
72°, 108°, 108°
108°, 108°, 72°
108°, 72°, 108°
none of these
In parallelogram ABCD, if ∠A = 2x + 25° and ∠B = 3x − 5°, then value of x will be :
x = 13°
x = 23°
x = 33°
x = 32°
ABCD is a parallelogram in which AB = 9.5 cm and its perimeter is 30 cm. Length of each side of parallelogram ABCD is :
AB = 9.5 cm, DC = 9.5 cm, BC = 5.5 cm, DA = 5.5 cm
AB = 9.5 cm, BC = 9.5 cm, DC = 5.5 cm, DA = 5.5 cm
DC = 5.5 cm, BC = 5.5 cm, AB = 9.5 cm, AD = 9.5 cm
none of these
Each side of a rhombus is 10 cm and one of its diagonals is 16 cm, length of other diagonal will be :
11 cm
12 cm
13 cm
15 cm