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Q1. If the degree measure of an angle is 30^o greater than twice the degree measure of its supplementary angle, what is the degree measure of the angle?

Solution

Let d = the degree measure of the angle. Then, 180^o - d = the degree measure of the supplement of the angle. We now set up an equation according to the question: d = 2 x (180^o - d) + 30^o We now solve for d: d = 360^o - 2d + 30^o (using distributive property) d + 2d = 360^o + 30^o (adding 2d on both sides) 3d = 360^o + 30^o (combining like terms) 3d = 390^o (dividing both sides by 3) d = 130^o Thus, the angle measures 130^o.

Q2. What is the measure of complement of each of the angle XYZ = 32o?

Solution

To find the complement of each of the given angle, we have to subtract them from 90^o, since the sum of two complementary angles is 90^o.Complementary angle the angle XYZ = 90^o - 32^o = 58^o.

Q3. What is the measure of supplement angle of the angle ABC of measure 88^o?

Solution

To find the supplement of each of the given angle, we have to subtract them from 180^o, since the sum of two supplementary angles is 180^o. Measure of supplement angle of angle ABC  = 180^o - 88^o  = 92^o.

Q4. What is the measure of complement of each of the following angle? (a) 45^o   (b) 54^o   (c) 65^o

Solution

To find the complement of each of the given angle, we have to subtract them from 90^o, since the sum of two complementary angles is 90^o. (a) 45^o Complementary angle of 45^o = 90^o - 45^o = 45^o (b) 54^o Complementary angle of 54^o = 90^o - 54^o = 36^o (c) 65^o Complementary angle of 65^o = 90^o - 65^o = 25^o

Q5. Give three examples each of (i) Parallel lines (ii) Intersecting lines from your environment.

Solution

Intersecting Lines : Adjacent sides of a cuboid, adjacent sides of a tennis court, adjacent side of a kite.   Parallel Lines : Railway lines, opposite edges of a cuboid, opposite sides of a football field.

Q6. Find the measure of angle 's', if the measure of angle s is 20 more than four times its supplement.

Solution

Given , angle = s (180^o - s) = supplement According to question, we get the equation as : s = 4 x (180 - s) + 20 s = 720 - 4s + 20 (using distributive property) 5s = 740 (add 4s on both sides) s = 148 (dividing both sides by 5) Thus, the measure of angle, s = 148^o

Q7. Identify which of the following pairs are complementary and which are supplementary. (a) 68^o, 112^o (b) 55^o, 35^o (c) 79^o, 101^o (d) 64^o, 26^o

Solution

In order to find the complementary pair of angles, add the angles to get 90^o. And to find the supplementary pair, the angle sum should amount to 180^o. (a) 68^o, 112^o Sum = 68^o + 112^o = 180^o Thus, it is a supplementary pair of angles. (b) 55^o, 35^oSum = 55^o + 35^o = 90^o Thus, it is a complementary pair of angles. (c) 79^o, 101^o Sum = 79^o + 101^o = 180^o Thus, it is a sumpplementary pair of angles. (d) 64^o, 26^o Sum = 64^o + 26^o = 90^o Thus, it is a complementary pair of angles.

Q8. Give one real life example where we can see a transversal.

Solution

A the signal or crossing we can see a transversal crossing the road.

Q9. Can we drawn a line passing through four points?

Solution

Yes we can we drawn a line passing through four points provided all the four points are collinear.

Q10. The measure of an angle supplement is 10 degrees more than 3 times more than that its complement. What is the measure of an angle?

Solution

let A = the angle then, (180 - A) = the supplement and (90 - A) = the complement the equation for the given statement: (180 - A) = 3 x (90 - A) + 10 180 - A = 270 - 3A + 10 (using distributive property) 3A - A = 280 - 180 (add 3A on both sides and subtract 180 ) 2A = 100 (combining like terms) A = 100/2 (dividing both sides by 2) A = 50^o is the angle.