Answer:
By comparing the ratios of sides in similar triangles ΔABC and ΔADB,we can say that 
Step-by-step explanation:
Given that ∠ABC=∠ADC, AD=p and DC=q.
Let us take compare Δ ABC and Δ ADB in the attached file , ∠A is common in both triangles
and given ∠ABC=∠ADB=90°
Hence using AA postulate, ΔABC ≈ ΔADB.
Now we will equate respective side ratios in both triangles.
Since we don't know BD , BC let us take first equality and plugin the variables given in respective sides.
Cross multiply
Hence proved.
Answer:
1. a= 7, A = 49 degrees
Side A = 7 , Side B = 24, Side C = 25
A= 49 degrees, C = 90 degrees , B=41
2. A= 4, B = 6.9, C=8
A= 22 degrees, B = 68, C= 90
3. A= 7, B = 14.4, C=16
A= 45 , B=45 , C=90
Answer:
54° and 110°
Step-by-step explanation:
The opposite angles of a cyclic quadrilateral are supplementary, sum to 180°
(9)
19x - 26 + 7x - 2 = 180
26x - 28 = 180 ( add 28 to both sides )
26x = 208 ( divide both sides by 26 )
x = 8
Then
∠ EFG = 7x - 2 = 7(8) - 2 = 56 - 2 = 54°
(10)
21x - 33 + 14x + 3 = 180
35x - 30 = 180 ( add 30 to both sides )
35x = 210 ( divide both sides by 35 )
x = 6
Then
∠ YVW = 14x + 3 = 14(6) + 3 = 84 + 3 = 87°
The inscribed angle YVW is half the measure of its intercepted arc YW, so
arc YW = 2 × 87° = 174°, then
arc XW = 174° - 64° = 110°
Answer:
354
Step-by-step explanation:
