Question

what is the value of the unknown in the figure and which property you used to find ?
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Answer 1

We have,

• To figure out the unknown value (x)

$\setlength{\unitlength}{1cm}\thicklines\begin{picture}(10,10) \put(3,0){ \vector( - 1,0){3}} \put(3,0){ \vector(1,0){3}} \put(3,0){ \vector( - 1,1){2}} \put(3,0){ \vector(1,1){2}} \qbezier(2.5,0)(2.3,0.2)(2.7,0.4) \qbezier(3.7,0)(3.8,0.4)(3.5,0.4) \qbezier(2.9,0.2)(3,0.3)(3.3,0.2) \put(2,0.2){ {75}^{ \circ} } \put(4,0.2){ {50}^{ \circ} }\put(3,0.5){ {x}^{ \circ} }} \put( - 0.3, - 0.2){ \large{A}}\put( 3, - 0.35){ \large{O}}\put( 6.1, - 0.2){ \large{B}}\put( 0.7, 2){ \large{P}}\put(5.1, 2){ \large{Q}} \end{picture}$

Here,

$\rm \angle{AOB} = 180 \degree \: \: \: \: \: \: \small \: \{ \texttt{AOB is a straight angle.}\}$

Also,

$\small \bf{}\angle{AOP} \blue+ \angle{ POQ} \blue+ \angle{QOB} = \angle{AOB} \\ \boxed{ \blue \bull \text{ \: putting \: \: the \: \: values}} \\ \rm \orange\leadsto \: 75 \degree \blue+ \green x \blue+ 50\degree = 180\degree \\ \boxed{ \blue\bull \text{ \:adding \: \: the \: \:possible \: \: terms}}\\ \rm \orange\leadsto \: 125\degree \blue+ \green x = 180 \\ \boxed{ \blue\bull \text{ \:transposing \: \: 125 \: \: to \: \: RHS}}\\ \rm \orange\leadsto \: \green x = (180 \blue- 125)\degree \\ \rm \orange{\leadsto} \: \green x = \red{55\degree}$

Hence,

• The unknown value of x is 55°.

〰️〰️Extra Information :

• A straight angle measures 180°
• A complete angle measures 360°
• A right angle measures 90°
• An acute angle measure ranges between 0° - 90°
• An obtuse angle measure ranges between 90° - 180°
• Complementary angles are those angles whose sum is 180°
• Supplementary angles are those angles whose sum is 360°