PLEASE ANSWER THESE BOTH QUESTIONS!!!
Answers
Answer:
Q.8
x = 90°
Q.9
a = 65°
b = 25°
Step-by-step explanation:
Q.8
We know that,
AP and DP are bisectors of ∠A' and ∠D'
∠A' = 2∠A
∠B' = 2∠B
In fig.2,
A'BCD' is a Quadrilateral,
Thus,
∠A' + ∠D' + 105° + 75° = 360° [Angle Sum Property]
2∠A + 2∠D + 105° + 75° = 360°
2(∠A + ∠D) + 180° = 360°
2(∠A + ∠D) = 360° - 180°
2(∠A + ∠D) = 180°
(∠A + ∠D) = 180°/2
(∠A + ∠D) = 90° ----- 1
Now,
In ΔAPD,
x + ∠A + ∠D = 180° [Angle Sum Property]
x + (∠A + ∠D) = 180°
From eq.1 we get,
x + 90° = 180°
x = 180° - 90°
x = 90°
Q.9
We know that,
In a rhombus, its opposite angles are equal.
Thus,
∠QPS = ∠QRS = 50°
Now,
The diagonals of rhombus also bisects its angles
Hence,
∠QRP = ∠PRS
Now,
∠QRS = ∠QRP + ∠PRS
∠QRS = ∠PRS + ∠PRS
∠QRS = 2 ×∠PRS
50° = 2 × b
2b = 50°
b = 50/2
b = 25°
Now,
we know that,
In a rhombus, the sum of 2 adjacent angles equals to 180.
∠QRS + ∠RQP = 180°
50° + ∠RQP = 180°
∠RQP = 180° - 50°
∠RQP = 130°
∠RQP = ∠RQS + ∠PQS
Similarly,
∠RQS = ∠PQS
So,
∠RQP = 2 × ∠RQS
130° = 2 × a
2a = 130°
a = 130/2
a = 65°
Hence,
a = 65°
b = 25°
Hope it helped and believing you understood it........All the best