Question

2 number pls give me answer stuck for hours

Answer 1

As ∠XYQ + ∠YXQ + ∠XQY = 180⁰

So, 35⁰ + 55⁰ + ∠XQY = 180⁰

Therefore ∠XQY = 90⁰

Then ∠XQZ will also be 90⁰

Therefore ∠a = 90⁰

Now,

PXY is a line segment which is 180⁰

So,

∠YXQ + ∠QXZ + ∠ZXP = 180⁰

Let's find ∠QXZ

90⁰ + 40⁰ + ∠QXZ = 180⁰

∠QXZ = 50⁰

Now,

∠YXQ + ∠QXZ + ∠ZXP = 180⁰

55⁰ + 50⁰ + ∠ZXP = 180⁰

∠ZXP = 75⁰

Therefore ∠b = 75⁰

Answer 2

Concept used

❖ Here the concept of exterior angle, Angle sum property and liner pair is used. ∠a can be found by adding ∠Y and ∠YXQ. Then we will find ∠QXZ by angle sum property. Then finally we can find ∠b by linear pair.

Let's proceed!

Solution

• Exterior angle property: it states that the measure of each exterior angle of a triangle is equal to the sum of the opposite angles.

• Angle sum property- the sum of the interior angles of triangle is 180°

• Linear pair - linear pair is formed when two 2 lines intersect at a single point. The sum of linear is 180°

$\bold{ \blue{Assume \: \: ∆XQY}}$

$\sf{ \implies∠a = ∠Y + ∠YXQ}$

$\sf{ \implies∠a= 35°+55°}$

$\sf{ \implies \red{∠a= 90°}}$

➹Therefore ∠a is 90°

$\bold{ \blue{Assume \: \: ∆XQZ}}$

$\sf{ \implies ∠Z+ ∠XQZ+∠QXZ= 180° \: \: \: \: \: \: [angle \: sum \: property]}$

$\sf{ \implies 40°+90°+∠QXZ= 180°} \\ \\ \sf{ \implies 130°+∠QXZ= 180°}$

$\sf{ \implies ∠QXZ=50°}$

$\sf{ \implies ∠YXQ+ ∠QXZ+ ∠PXZ= 180° \: \: \: \: \: [liner \: pair]}$

$\sf{ \implies 55°+50°+∠PXZ=180°} \\ \\ \sf{ \implies∠PXZ= 180°-105°}$

$\sf{ \implies \red{∠PXZ= 75°}}$

➹Therefore ∠b is 75°

---------------------------------------------------