Question

The larger of two supplementary angles exceeds the smaller by 54º. The angles
are:​

Answer 1

Step-by-step explanation:

The larger of two supplementary angles exceeds the smaller by 54º. The angles

are:

let the smaller angle be = x

therefore the larger angle be = x + 54°

ATQ

sum of supplementary angle is 180°

→ x + x + 54° = 180°

→ 2x = 180° - 54°

→ 2x = 126°

→ x = 126° ÷ 2

x = 63°

→ smaller angle = x = 63°

→ larger angle = x + 54° = 63° + 54° = 117°

Answer 2

Answer:

The angles are 117° and 63°.

Step-by-step explanation:

Given:

Larger of the two supplementary angles is 54° more than the smaller angle.

To find :

The angles

Solution :

Let the angles be,

• Larger angle as x
• Smaller angle as y

The larger angle exceeds the smaller angle by 54°.

The angles are supplementary. Supplementary angles are angles whose sum is 180°.

So, the equations formed are -

$\longrightarrow$ x + y = 180° ---- (Eq. 1)

$\longrightarrow$ y + 54° = x ---- (Eq. 2)

_____________________________

Substitute equation 2 in equation 1,

$\longrightarrow$ (y + 54) + y = 180

$\longrightarrow$ 2y + 54 = 180

$\longrightarrow$ 2y = 180 - 54

$\longrightarrow$ 2y = 126

$\longrightarrow$ y = 126/2

$\longrightarrow$ y = 63°

Smaller angle = 63°

_____________________________

★ Larger angle =

Substitute value of y in equation 2,

$\longrightarrow$ 63 + 54 = x

$\longrightarrow$ 117° = x

Larger angle = 117°

Therefore, the angles are 117° and 63°.