Question

Hi all need the answers for following questions

Answer 1

Solution 1

Framing an equation we get,

$\longrightarrow \tt \: 5p \degree + (3p - 20)\degree = 180\degree \\ \\ \\ \longrightarrow \tt 5p \degree + 3p\degree - 20\degree = 180\degree \\\\\\ \longrightarrow \tt 5p\degree + 3p\degree = 180\degree + 20\degree \\ \\ \\ \longrightarrow \tt 5p\degree + 3p\degree = 200\degree \\ \\ \\ \longrightarrow \tt 8p\degree = 200\degree \: \: \\ \\ \\ \longrightarrow \tt p = \cancel\frac{200}{8} \\ \\ \\ \longrightarrow { \blue{ \boxed{ \frak{p = 25\degree }} \star}} \: \:$

• Henceforth the value of P is 25°

Solution 2]

$\longrightarrow \tt (33 - q)\degree + (3q + 5)\degree = 90\degree \\ \\ \\ \longrightarrow \tt 33 - q+ 3q + 5 = 90\degree \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt 38 + 2q = 90\degree \\ \\ \\ \longrightarrow \tt 2q = 90 - 38 \\ \\ \\ \longrightarrow \tt 2q = 52\degree \\ \\ \\ \longrightarrow \tt q = \cancel\frac{52}{2} \\ \\ \\ \longrightarrow \tt { \blue{ \boxed{ \frak{q = 26 \degree }} \star}} \: \:$

${ \blue{ \boxed{ \tt{Question \: 3 }}}}$

Given:

• In the given figure P||Q

To Find:

• The unknown angles in the figure

Solution :

Now,

• Let's use suitable properties and find the angles

$\leadsto \tt 130\degree + \angle e = 180\degree[adjacent \: angles] \\ \\ \\ \leadsto \tt \: \angle e = 180\degree - 130\degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \leadsto \tt \: \angle e = { \pink{ \boxed{ \tt{50}}\degree}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the measure of angle e is 50°

$\leadsto \tt\angle e = \angle f \: [vertically \: opposite \: angles]\\ \\ \\ \leadsto \tt \: \angle 50\degree = \angle f \\ \\ \\ \leadsto \tt\angle f = { \pink{ \boxed{ \tt{50}}\degree}}$

• Henceforth the measure of angle f is 50°

$\leadsto \tt\angle f = \angle a[opposite \: interior \: angles] \\ \\ \\ \leadsto \tt\angle 50 \degree = \angle a \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \leadsto \tt\angle a = { \pink{ \boxed{ \tt{50}}\degree}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the measure of angle a is 50°

$\leadsto \tt\angle a = \angle c \: [vertically \: opposite \: angles]\\ \\ \\ \leadsto \tt \: \angle 50\degree = \angle c \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \leadsto \tt\angle c = { \pink{ \boxed{ \tt{50}}\degree}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the Measure of angle c is 50°

$\leadsto \tt \: \angle a \degree + \angle d = 180\degree[adjecent \: angles] \\ \\ \\ \leadsto \tt \: \angle 50 + \angle d = 180\degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \leadsto \tt \:\angle d = 180\degree - 50\degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \leadsto \tt \: \angle d= { \pink{ \boxed{ \tt{130}}\degree}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the measure of angle d is 130°

$\leadsto \tt\angle d = \angle b \: [vertically \: opposite \: angles]\\ \\ \\ \leadsto \tt \: \angle 130\degree = \angle b \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \leadsto \tt\angle b = { \pink{ \boxed{ \tt{130}}\degree}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Henceforth the measure of angle b is 130°

${ \blue{ \boxed{ \tt{Question \: 4 }}}}$

A]

Given:

• ∠ABC measures 70°

To Find:

• the measure of ∠x

Solution:

Using the identity

• Corresponding angles are equal

$\leadsto \tt\angle \: b = \angle g \\ \\ \\ \leadsto \tt\angle 70\degree = \angle g \\ \\ \\ \leadsto \tt\angle g = { \pink{ \boxed{ \tt{70}}\degree}}$

• Henceforth the measure of angle G is 70°

$\leadsto \tt\angle g = \angle x \: \: \: \\ \\ \\ \leadsto \tt\angle 70\degree = \angle x \\ \\ \\ \leadsto \tt\angle x = { \pink{ \boxed{ \tt{70}}\degree}}$

• Therefore the measure of angle x is 70°

• Due to word limit I couldn't post the whole answer so some of the parts are in the attachment!

[ Note: Solution 4 part b is in the attachment]