Question

In the adjoining figure, | | m and n is a transversal. If angle a = (2x - 8)° and angle b= (3x - 7)° , find the measures of a and b.​

Answer 1

Step-by-step explanation:

its my pleasure to help you.

please mark me as a brainliest

Answer 2

Given:-

• l || m and n is a transversal.

• $\sf{\angle{a} = (2x - 8)^{\circ}}$ and $\sf{\angle{b} = (3x - 7)^{\circ}}$

To Find:-

• The Value of a and B

Concept Used:-

• When two lines are Parallel and traversed by a line then sum of two Consecutive angle is equal to 180°. This Property is known co - interior angle Property.

Now,

→ $\sf{\angle{a} + \angle{b} = 180^{\circ}}$

→ $\sf{ (2x - 8)^{\circ} + (3x - 7)^{\circ} = 180^{\circ}}$

→ $\sf{ 2x - 8 + 3x - 7 = 180}$

→ $\sf{ 5x - 15 = 180}$

→ $\sf{ 5x = 180 + 15}$

→ $\sf{ 5x = 195}$

→ $\sf{ x = \dfrac{195}{5}}$

→ $\sf{ x = 39}$

Hence, The Value of x is 39.

Putting the Value of x.

→ (2x - 8)° → 2 × 39 - 8 → 70°

→ (3x - 7)° → 3 × 39 - 7→ 110°

Hence, The Value of a and b is 70° and 110° respectively.