Question

Find the measure of the unknown angles in the following figures.
please do answer my question.​

Answer 1

Answer:

(a) x° = 138°

(b) a° = 30° and b° = 82°

(d) y° = 98°

(e) x° = 60°

Step-by-step explanation:

(a) Sum of all angles of a triangle = 180 °

Measure of two angles are given. Let the third angle be y°

So,

60 + 78 + y° = 180

138° + y° = 180°

y° = 180° - 138° = 42°

Now, x° + y° = 180°   these are supplementary angles.

x° = 180 - y° = 180 - 42 = 138°

∴ x° = 138°

(b) 30° = a°   these are vertically opposite angles.

a° + b° + 68° = 180°   Angle sum property of Δ

30 + 68 + b° = 180°

98° + b° = 180°

So, b° = 82°

∴ a° = 30° and b° = 82°

(d) 45 + 37 + y° = 180     angle sum property

82° + y° = 180°

∴ y° = 98°

(e) This is an equilateral triangle. And the measure of all angles of an equilateral triangle is equals to 60°.

∴ x° = 60°