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Question

In figure, the sides QP and RQ of $triangle P Q R$ are produced to points S and T respectively. If $stack S P R with _ below equals 135 to the power of ring operator end exponent$ and $open floor P Q T equals 110 to the power of ring operator end exponent close$ then $stack P R Q with _ below equals$

65°
55°
45°
75°

hint Hint:

The fundamental geometric shapes are lines and angles. Infinite points that stretch infinity in both directions make up lines, which are geometric objects. Straight lines with little depth or width are present. Here we have given the sides QP and RQ of $triangle P Q R$ are produced to points S and T respectively and $stack S P R with _ below equals 135 to the power of ring operator end exponent$ and $open floor P Q T equals 110 to the power of ring operator end exponent close$ We have to find angle PQR.

The correct answer is: 65°

A line is a simple, one-dimensional shape that can go on forever in the opposing directions. A line may be vertical or horizontal. It can be drawn either top to bottom or left to right.
When the ends of two rays collide at a single location, an angle is the geometry that results. They are expressed as radians or degrees (°). A 360-degree angle is the same as a whole rotation. It is symbolised by the character "∠".
Here we have given the sides QP and RQ of $triangle P Q R$ are produced to points S and T respectively and $stack S P R with _ below equals 135 to the power of ring operator end exponent$ and $open floor P Q T equals 110 to the power of ring operator end exponent close$ .
$N o w space w e space h a v e colon space angle T Q P plus angle P Q R equals 180 degree space left parenthesis l i n e a r space p a i r right parenthesis P u t t i n g space t h e space v a l u e s space i n space i t comma space w e space g e t colon 110 degree plus angle P Q R equals 180 degree angle P Q R equals 180 degree minus 110 degree angle P Q R equals 70 degree S i l i m a r l y comma space w e space h a v e colon angle S P R plus angle R P Q equals 180 degree space left parenthesis l i n e a r space p a i r right parenthesis 135 degree plus angle R P Q equals 180 degree space angle R P Q equals 180 degree minus 135 degree angle R P Q equals 45 degree N o w space w e space k n o w space t h a t space i n space t r i a n g l e comma space t h e space t o t a l space a n g l e space s u m space i s space 180 space d e g r e e comma space s o colon I n space t r i a n g l e space P Q R comma space w e space h a v e colon angle P plus angle Q plus angle R equals 180 degree 45 plus 70 plus R equals 180 R equals 180 minus 115 R equals 65$

Here we used the concept of linear pair and angle sum property of a triangle. When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. So here the angle PRQ is 65 degrees.

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65°
55°
45°
75°

The correct answer is: 65°

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Can’t find what you’re looking for?

In figure, the sides QP and RQ of are produced to points S and T respectively. If and then

65° 55° 45° 75°

The correct answer is: 65°

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