Question

Find the measure of angle A

Answer 1

Answer:

angle B = 180 - 110 = 70 degrees

angle C = 180 - 120 = 60 degrees

Sum of all three angle of a triangle = 180 degrees

A + B + C = 180

A + 70 + 60 = 180

A + 130 = 180

A = 180 - 130

Thus, angle A = 50 degree.

Hope this helps you☺

Answer 2

Given:

• ∠CBX = 110°

• ∠ACY = 120°

To Find:

• ∠BAC.

Concept Used:

• Linear Pairs.

Solution:

• We're asked to find ∠A.

We can find it's value if we have the angle measures of B & C.

We will be able to find ∠B & ∠C with the help of the other angles given to us.

We know that;

⇒ ∠CBA + ∠CBX = 180° (Linear Pair)

⇒ ∠CBA + 110° = 180°

⇒ ∠CBA = 180° - 110°

⇒ ∠CBA = 70°

i.e, ∠B = 70°

Similarly;

⇒ ∠ACB + ∠ACY = 180° (Linear Pair)

⇒ ∠ACB + 120° = 180°

⇒ ∠ACB = 180° - 120°

⇒ ∠ACB = 60°

i.e, ∠C = 60°

In ΔABC,

⇒ ∠A + ∠B + ∠C = 180° (ASP of a Δ)

⇒ ∠A + 70° + 60° = 180°

⇒ ∠A + 130° = 180°

⇒ ∠A = 180° - 130°

⇒ ∠A = 50°

Final Answer:

∠A = 50°