If X is a point on the line AB- Y and Z are points outside such that - AXY - 45- and - YXZ - 150- then - AX Z is equal to

The correct option is D 165 ^∘ ∠ YXB = 180^∘ ∠ AXY ......(linear pair) #160; #160; #160; #160; #160; #160; #160; #160; #160; ...

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Byju's Answer

Standard IX

Mathematics

Any Point Equidistant from the End Points of a Segment Lies on the Perpendicular Bisector of the Segment

If X is a poi...

Question

If X is a point on the line AB, Y and Z are points outside such that $∠ A X Y = 45^{\circ}$ and $∠ Y X Z = 150^{\circ}$ , then $∠ A X Z$ is equal to

120

^{\circ}

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135

^{\circ}

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150

^{\circ}

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165

^{\circ}

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Solution

The correct option is D 165 $^{\circ}$
$∠ Y X B = 180^{\circ} - ∠ A X Y$ ......(linear pair)

$= 180^{\circ} - 45^{\circ} = 135^{\circ}$

$∴$ $∠ B X Z = ∠ Y X Z - ∠ Y X B$

$= 150^{\circ} - 135^{\circ} = 15^{\circ}$

Hence $∠ A X Z = 180^{\circ} - ∠ B X Z$ .......(linear pair)

$= 180^{\circ} - 15^{\circ} = 165^{\circ}$

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If X is a point on the line AB, Y and Z are points outside such that ∠AXY=45∘ and ∠YXZ=150∘, then ∠AXZ is equal to

The correct option is D 165∘∠YXB=180∘−∠AXY......(linear pair) =180∘−45∘=135∘∴ ∠BXZ=∠YXZ−∠YXB =150∘−135∘=15∘Hence ∠AXZ=180∘−∠BXZ.......(linear pair) =180∘−15∘=165∘

If X is a point on the line AB, Y and Z are points outside such that $∠ A X Y = 45^{\circ}$ and $∠ Y X Z = 150^{\circ}$ , then $∠ A X Z$ is equal to