Question 105(ii)

In the given PQ, RS and UT are parallel lines.

If c $= 75^{\circ} a n d a = \frac{2}{5} c,$ find b.

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Solution

Since, $P Q | | U T a n d P T$ is transversal.
Therefore, $∠ Q P T = ∠ U T P [a l t e r n a t e i n t e r i o r a n g l e s] \Rightarrow a + b = c \Rightarrow b = c - a \Rightarrow b = c - \frac{2}{5} c [∴ a = \frac{2 c}{5}, g i v e n] \Rightarrow b = \frac{5 c - 2 c}{5} \Rightarrow b = \frac{3 c}{5} \Rightarrow b = \frac{3 \times 75^{\circ}}{5} [∴ c = 75^{\circ}] \Rightarrow b = 45^{\circ}$

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Question 105(i)

In the given figure, PQ, RS and UT are parallel lines.

If $c = 57^{\circ} a n d a = \frac{c}{3}$ , find the value of d.

c = 57^{\circ} a n d a = \frac{c}{3}

Question 75

In the given figure PQ|| RS, TR|| QU and $∠ P T R = 42^{\circ}$ . Find $∠ Q U R .$

Question 75

In the given figure PQ|| RS, TR|| QU and $∠ P T R = 42^{\circ}$ . Find $∠ Q U R .$

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