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zhenek [66]
3 years ago
10

Number 3 I don’t understand it

Mathematics
1 answer:
yuradex [85]3 years ago
5 0
The measures of complementary angles add up to 90 degrees. Angles A and B therefore add up to 90 degrees.

To find the value of x, set the sum of (the measures of) A and B to 90 (degrees), and solve algebraically.

m∠A + m∠B = 90°
(3x + 5)° + (2x - 15)° = 90°

5x - 10 = 90
5x = 100

x = 20

Then, plug the value of x back into each expression to find the measures of angles A and B.

m∠A = (3x + 5)°
m∠A = (3(20) + 5)°
m∠A = (60 + 5)°

m∠A = 65°

m∠B = (2x - 15)°
m∠B = (2(20) - 15)°
m∠B = (40 - 15)°

m∠B = 25°

You can check to make sure that the angles are complementary by adding them together. Their measures should equal to 90°.

65° + 25° = 90°
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A quadrilateral in which both pairs of opposite sides are parallel is called a <u>Parallelogram</u>

Step-by-step explanation:

A quadrilateral is said to be  parallelogram if

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From the question given above

<u>ABCD is a parallelogram and P and Q are points on BD such that</u>

<u>DP=QB</u>

In ΔAPD and ΔCQB,--------------------------(i)

DP = QB (Given)

∠ADP = ∠CBQ (Alternate interior angles)

AD = BC

(Hence it is proved that -Opposite sides of a parallelogram are equal)

so, ΔAPD ≅ ΔCQB    (As per  SAS congruence rule)

 If , ΔAPD ≅ ΔCQB.-------------------------(ii)

AP = CQ               ( by CPCT )

 In ΔAQB and ΔCPD,-----------------------(iii)

BQ = DP (Given)

∠ABQ = ∠CDP (Alternate interior angles)

AB = CD  (Opposite sides of a parallelogram)

so, ΔAQB ≅ ΔCPD                       (As per  SAS congruence rule)

(iv) AQ = CP              (According to  CPCT as ΔAQB ≅ ΔCPD.)

 From (ii)  and (iv) equation ,we can say that

AP=CQ ,

AQ=CP

<u> It is proved that APCQ has equal opposite sides also it has equal opposite angles. </u><u>Hence,APCQ is a Parallelogram</u>

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