Question

find the value of x and the measure of each angle ​

Answer 1

Step-by-step explanation:

By property of exterior angle of triangle

4x+2+2x+9 = 5x+13

x = 2

Angle C = 10°. Angle D = 13°

Angle ABD = 23°

ANGLE CBD = 157°

Answer 2

Given,

Angle ABD = (5x+13)°

Angle BCD = (4x+2)°

Angle BDC = (2x+9)°

To find,

The value of x and the measure of each angle.

Solution,

The value of x will be 2 and the measure of angle ABD will be 23°, angle BCD will be 10°, angle BDC will be 13° and angle DBC will be 157°.

We can easily solve this problem by following the given steps.

Now, we know that according to the property of exterior angle, the exterior angle in a triangle is equal to the sum of its opposite angles in a triangle.

So,

Angle ABD = Angle BCD + angle BDC

(5x+13)° = (4x+2)° + (2x+9)°

= 6x+11

5x+13-11 = 6x ( Moving 11 from the right-hand side to the left-hand side results in the change of the sign from plus to minus.)

5x+2 = 6x

6x-5x = 2

x = 2

Putting the value of x in the given angles,

Angle ABD = (5x+13)°

Angle ABD = (5×2+13)°

Angle ABD = (10+13)°

Angle ABD = 23°

Angle BCD = (4x+2)°

Angle BCD = (4×2+2)°

Angle BCD = (8+2)°

Angle BCD = 10°

Angle BDC = (2x+9)°

Angle BDC = (2×2+9)°

Angle BDC = (4+9)°

Angle BDC = 13°

Now, we know that the angle made on a straight line is 180°. And AC is a line.

So,

angle DBC = (180-angle ABD)°

angle DBC = (180-23)°

angle DBC = 157°

Hence, the value of x is 2 and the measure of angle ABD 23°, angle BCD is 10°, angle BDC is 13° and angle DBC 157°.