In Fig. PQ || RS. If 1= (2a + b)^ and 6= (3a - b)^ , then the measure of 2 in terms of b is:

In Fig. PQ || RS. If 1= (2a + b)^ and 6= (3a - b)^ , then the mea…

MCQ

In Fig. $PQ || RS.$ If $\angle1= (2\text{a} + \text{b})^\circ$ and $\angle6= (3\text{a} - \text{b})^\circ$, then the measure of $\angle2$ in terms of $b$ is:

A
$(2 + b)^\circ$
B
$(3 – b)^\circ$
✓
$(108 – b)^\circ$
D
$(180 – b)^\circ$

✓

Answer

Correct option: C.

$(108 – b)^\circ$

From them given figure, $\angle1=\angle5$ [Corresponding angle]
$\Rightarrow\angle5 = (2\text{a}+\text{b})^\circ$
$[\because\angle1=(2\text{a}+\text{b})^\circ,\text{given}]$
Also, $\angle5+\angle6=180^\circ$ [liner paire]
$\Rightarrow (2\text{a} + \text{b})^\circ + (3\text{a} - \text{b})^\circ = 180^\circ$
$[\because\angle6=(3\text{a}-\text{b})^\circ,\text{given}]$
$\Rightarrow(2\text{a} + 3\text{a}) + (\text{b} - \text{b}) = 180^\circ$
$\Rightarrow5\text{a} = 180^\circ$
$\Rightarrow\text{a}=\frac{180^\circ}{5}$
$\Rightarrow \text{a} = 36^\circ$
Now, $\angle1+\angle2=180^\circ$ [liner paier]
$\Rightarrow\angle2=180^\circ-\angle1$
$\Rightarrow\angle2=180^\circ-(2\text{a}+\text{b})^\circ$
$[\because\angle1=(2\text{a}+\text{b})^\circ,\text{given}]$
$\Rightarrow\angle2=180^\circ-2\text{a}-\text{b}$
$\Rightarrow\angle2=180^\circ-2\times36^\circ-\text{b}$
$[\because\ \text{a}=36^\circ]$
$\Rightarrow\angle2=180^\circ-72^\circ-\text{b}$
$\Rightarrow\angle2=(180^\circ-\text{b})^\circ$