Question

x,
38 degree m find the marked with small letters
​

Answer 1

Answer:

x= 56, y= 56

Step-by-step explanation:

Answer:

1. x=69

2. a=51, b=39

3. x=56, y=56

4. a=67

Step-by-step explanation:

1. Rectangle:

The diagonals of rectangle are congruent and bisect each other.

m\angle OAB=m\angle OBA=21^{\circ}m∠OAB=m∠OBA=21

∘

All interior angle of a rectangle are right angles. So,

m\angle OBA+x=90m∠OBA+x=90

21+x=9021+x=90

x=90-21x=90−21

x=69x=69

2. Rectangle:

Similarly,

m\angle ORS=m\angle OSR=bm∠ORS=m∠OSR=b (Definition of rectangle)

m\anlge ROS=m\angle POQ=102m\anlgeROS=m∠POQ=102 (Vertical angles)

m\angle POS+m\angle ORS+m\angle OSR=180m∠POS+m∠ORS+m∠OSR=180 (Angle sum property)

102+b+b=180102+b+b=180

2b=180-1022b=180−102

2b=782b=78

b=39b=39

a+b=90a+b=90 (Right angle)

a+39=90a+39=90

a=90-39a=90−39

a=51a=51

3. Rhombus:

Diagonals of a rhombus are perpendicular bisectors.

m\angle PLQ=90m∠PLQ=90 (Definition of rhombus)

m\angle PLQ+m\angle LPQ+m\angle LQP=180m∠PLQ+m∠LPQ+m∠LQP=180 (Angle sum property)

90+34+x=18090+34+x=180

124+x=180124+x=180

x=180-124x=180−124

x=56x=56

m\angle PQS=m\angle PSQm∠PQS=m∠PSQ (Property of isosceles triangle)

x=yx=y

y=56y=56

4. square:

Diagonals of square are angle bisector.

m\angle XCD=m\angle XCY=45m∠XCD=m∠XCY=45 (Definition of square)

m\angle YXC+m\angle CXD=180m∠YXC+m∠CXD=180 (Supplementary angles)

m\angle YXC+112=180m∠YXC+112=180

m\angle YXC=180-112m∠YXC=180−112

m\angle YXC=68m∠YXC=68

m\angle YXC+m\angle XCY+m\angle XYC=180m∠YXC+m∠XCY+m∠XYC=180 (Angle sum property)

68+45+a=18068+45+a=180

113+a=180113+a=180

a=180-113a=180−113

a=67a=67

Thank you

Answer 2

Answer:

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