Question

Fint the unknown
marked angle
by ​

Answer 1

iv)let angle ABC be a° and angle ACB be b°.

here,

a°+110°=180°[linear pair]

or,a°=180°-110°

∴ a°=70°

b°=a°[base angles of a isosceles triangle]

b°=70°

a°+b°+y°=180°[sum of all angles of a triangle]

or,70°+70°+y°=180°

or,140°+y°=180°

∴ y°=40°

b°+x°=180°[linear pair]

or,70°+x°=180°

∴ x°=110°

ans

Answer 2

Figure (iv)

We can find the value of x using the exterior angle theorem which states that exterior angle of a triangle is equal to the sum of two non adjacent interior angles.

Let us find ∠ABC,

⇒ ∠ABC + 110° = 180° [ ABE is a straight line ]

⇒ ∠ABC = 70° ...(1)

Now, As the given exterior angle theorem above, we have

⇒ ∠ACD = ∠BAC + ∠ABC

⇒ x = y + 70° ...(2) [ from (1) ]

Referring to the same triangle, we have

⇒ AB = AC

which means

⇒ ∠ABC = ∠ACB

Because angles opposite to equal sides are also equal.

So,

⇒ ∠ABC = ∠ACB

⇒ 70° = 180° - x [ BCD is a straight line ]

⇒ x = 180° - 70°

⇒ x = 110°

Now, Substituting value of x in (1),

⇒ x = y + 70°

⇒ 110° - 70° = y

⇒ y = 40°

Hence, Values of:

• x = 110°
• y = 40°

Figure (vi)

In the given, we are given

• AB = AC
• ∠BAC = 40°

Since, AB = AC, which means the angles opposite to these two sides are also equal,

⇒ ∠ABC = ∠ACB

⇒ 180° - x = 180° - y

[EBD & DCE are straight lines]

⇒ -x = -y

⇒ x = y ...(1)

Now, In ∆ABC,

⇒ Sum of all Interior angles = 180°

⇒ ∠ABC + ∠BAC + ∠ACB = 180°

⇒ 180° - x + 40° + 180° - y = 180°

⇒ -x - x = -220° [ from (1), x = y ]

⇒ -2x = -220°

⇒ x = 110°

Since, x = y from (1),

Therefore, y = 110°

Hence, we have

• x = 110°
• y = 110°