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Standard VII

Mathematics

Adjacent Angles

In a pair of ...

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Question 29

In a pair of adjacent angles, (i) vertex is always common (ii) one arm is always common, and (iii) uncommon arms are always opposite rays. then
(a) all (i), (ii) and (iii) are true
(b) (iii) is false
(c) (i) is false but (ii) and (iii) are true
(d) (ii) is false

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Solution

Two angles are called adjacent angles, if they have a common vertex and a common arm but no common interior points. It is not necessary that uncommon arms must be always opposite rays.

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Question 29

In a pair of adjacent angles, (i) vertex is always common (ii) one arm is always common, and (iii) uncommon arms are always opposite rays. then
(a) all (i), (ii) and (iii) are true
(b) (iii) is false
(c) (i) is false but (ii) and (iii) are true
(d) (ii) is false

Q. Consider the following statements:
I. If the roots of the equation

a x^{2} + b x + c = 0

are negative reciprocal of each other, than a + c = 0.
II. A quadratic equation can have at all most two roots.
III. If α, β are the roots of

x^{2} - 22 x + 105 = 0,

then α + β = 22 and α − β = 8.

Of these statements:
(a) I and II are true and III is false.
(b) I and III are true and II is false.
(c) II and III are true I is false.
(d) I, II and III are all true.

Q. Statement -

I

\to L = I \to ω

is always true for bodies of all shapes.
Statement-

II

\to τ = \frac{d \to L}{d t}

is always true in inertial frames.

$△$ ABC is an acute angled triangle. DE is drawn parallel to BC as shown. Which of the following are always true?

i) $△ A B C \sim △$ ADE

ii) $\frac{A D}{B D} = \frac{A E}{E C}$

iii) $D E = \frac{B C}{2}$

Question 23

Statements (I) and (II) are as given below:
I: If two lines intersect, then the vertically opposite angles are equal.
II: If a transversal intersects two other lines, then the sum of two interior angles on the same side of the transversal is $180^{\circ}$ .

Then,
(a) both (I) and (II) are true
(b) (I) is true and (II) is false
(c) (I) is false and (II) is true
(d) both (I) and (II) are false

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Adjacent Angles

Standard VII Mathematics

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Question 29 In a pair of adjacent angles, (i) vertex is always common (ii) one arm is always common, and (iii) uncommon arms are always opposite rays. then (a) all (i), (ii) and (iii) are true (b) (iii) is false (c) (i) is false but (ii) and (iii) are true (d) (ii) is false

Two angles are called adjacent angles, if they have a common vertex and a common arm but no common interior points. It is not necessary that uncommon arms must be always opposite rays.

Question 29

In a pair of adjacent angles, (i) vertex is always common (ii) one arm is always common, and (iii) uncommon arms are always opposite rays. then
(a) all (i), (ii) and (iii) are true
(b) (iii) is false
(c) (i) is false but (ii) and (iii) are true
(d) (ii) is false