(i)
∠BAD + ∠ABD + ∠ADB = 180 <em>the sum of the angles of a triangle equals 180°</em>
70 + 50 + ∠ADB = 180 <em>substituted given information</em>
∠ADB = 60 <em>subtraction property (subtracted 70 and 50)</em>
∠ABD + ∠BDC = ∠ADC <em>angle addition property</em>
60 + ∠BDC = 80 <em>substituted solved and given information</em>
∠BDC = 20 <em>subtraction property</em>
(ii) SORRY but I'm not sure how to find ∠BCD. If ∠ADC = ∠ABC, then ∠DBC = 30. We already calculated ∠BDC = 20, which means that ∠BCD = 130
(iii)
∠BCA = ∠ADB <em>given as a hint</em>
∠BCA = 60 <em>substituted ∠ADB that was solved in part (i)</em>
Answer: (i) = 20, (ii) = 130?, (iii) = 60
<u>Solution-</u>
Given that,
In the parallelogram PQRS has PQ=RS=8 cm and diagonal QS= 10 cm.
Then considering ΔPQT and ΔSTF,
1- ∠FTS ≅ ∠PTQ ( ∵ These two are vertical angles)
2- ∠TFS ≅ ∠TPQ ( ∵ These two are alternate interior angles)
3- ∠TSF ≅ ∠TQP ( ∵ These two are also alternate interior angles)
<em>If the corresponding angles of two triangles are congruent, then they are said to be similar and the corresponding sides are in proportion.</em>
∴ ΔFTS ∼ ΔPTQ, so corresponding side lengths are in proportion.
As QS = TQ + TS = 10 (given)
If TS is x, then TQ will be 10-x. Then putting these values in the equation
∴ So TS = 3.85 cm and TQ is 10-3.85 = 6.15 cm
Answer:
38 inches
Step-by-step explanation:
since we are finding the diagonal we are going to use the equation a^2+b^2=c^2
so if we do substitution we would have 32^2+20^2=C^2
32^2= 1024
20^2= 400
so,
1024 + 400 = C^2
1424 = C^2
to get rid of the C^2 we have to take the square root of it. But whatever we do on one side of the equation we have to do on the other side so,
C = sqrt(1424)
C = 37.73
C = 38 inches
Answer:
Step-by-step explanation:
Answer:
B
7! = 7 X 6 X 5 X 4 x 3 x 2 x 1
Step-by-step explanation:
n! is the product of all natural numbers until n
7! = 1 × 2 × 3 × 4 × 5 × 6 × 7