MATH SOLVE

2 months ago

Q:
# PLEASE HELP ASAP WILL GIVE BRAINLIEST 5 STAR RATING THANKS AND BRAINLIEST!ONLY TO THE CORRECT ANSWERER(S)! 98 POINTS! for BRAINLIEST!!!!YOU MUST ANSWER ALL 5 QUESTIONS AND PROPERLY, NO WORK NEEDED.

Accepted Solution

A:

Answer:Q1. y = 3Q2. m∠B = 125°Q3. m∠SPQ = 110°Q4. x = 55Q5. x = 123Step-by-step explanation:Q1.If ABCD is a rectangle, then diagonals are congruent: AC = BD.We haveAC = 5y - 2BD = 4y + 1Substitute:5y - 2 = 4y + 1 add 2 to both sides5y - 2 + 2 = 4y + 1 + 25y = 4y + 3 subtract 4y from both sides5y - 4y = 4y - 4y + 3y = 3Q2.In a parallelogram opposite angles are congruent. Therefore m∠D = m∠B.We have m∠D = 125° → m∠B = 125°Q3.In the rhombus, the diagonals are bisectors of the rhombus angles.Therefore ∠SPR and ∠QPR are congruent.We havem∠SPR = (2x +15)°m∠QPR = (3x - 5)°The equation:2x + 15 = 3x - 5 subtract 15 from both sides2x + 15 - 15 = 3x - 5 - 152x = 3x - 20 subtract 3x from both sides2x - 3x = 3x - 3x - 20-x = -20 change the signsx = 20Substitute it to the expression m∠SPR = (2x + 15)°:m∠SPR = (2(20) + 15)° = (40 + 15)° = 55°m∠SPR = m∠QPR → m∠QPR = 55°∠SPQ = ∠SPR + ∠QPR → m∠SPQ = 2(55°) = 110°Q4.In the parallelogram, the sum of the angle measures on one side is 180°.Therefore we have the equation:(2x + 15) + x = 180 combine like terms(2x + x) + 15 = 180 subtract 15 from both sides3x + 15 - 15 = 180 - 153x = 165 divide both sides by 33x/3 = 165/3x = 55Q5.In a parallelogram opposite angles are congruent. Therefore z = y and x = 2z + 9 → x = 2y + 9 (*)In the parallelogram, the sum of the angle measures on one side is 180°.Therefore x + y = 180 (**)Substitute (*) to (**)(2y + 9) + y = 180 combine like terms(2y + y) + 9 = 180 subtract 9 from both sides3y + 9 - 9 = 180 - 93y = 171 divide both sides by 3y = 57Put it to (*):x = 2(57) + 9x = 114 + 9x = 123