Question

please help me with these questions
ans with steps...

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Answer 1

Answer:

1. y = 80

2. x = 110

Step-by-step explanation:

1. ∠PRS and 135° are supplementary

∠PRS = 180-135=45

∠QRS = 55° + ∠PRS = (55 + 45)° = 100°

∠P + ∠Q + ∠QRS + ∠S = 360°                             (Using angle sum property)

⇒ (90 + 90 + 100 + ∠Y)° = 360°                            (Given)

⇒ ∠Y + 280 = 360

⇒ ∠Y = 360 - 280 = 80

∴ ∠Y = 80°

2.  ∠ABC = 105°                                                     (Using angle sum property)

∠CBD = 75°                                                            (Supplementary angles)

∠X = 35 + 75                                                          (External angle property)

= 110°

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Answer 2

Answer:

1) Y= 80 °, 2) 110°

Step-by-step explanation:

ANS 1.) In ∆ RPQ

angle RQP + PRQ + RPQ = 180°

90° + 55° + angle RPQ = 180°

angle RPQ = 180° - ( 90° + 55° )

angle RPQ = 45°

IN ∆ SPR

angle SPR + RPQ = 90° ( GIVEN )

angle SPR = 90° - RPQ = 45°

angle SPR + Y = 135° ( EXTERIOR ANGLE SUM PROPERTY)

angle Y = 135° - 45° = 80°

ANS 2.) IN ∆ ABC

angle ACB + angle BAC + angle ABC = 180° ( SUM OF INTERIOR ANGLES OF ∆ )

25° + 50° + angle ABC = 180°

angle ABC = 180° - 75° = 105°

Now in ∆BDE

angle EBD + ABC = 180° ( linear pair )

angle EBD = 75°

angle x = angle EDB + EBD

x = 75° + 35° = 110°

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