Question

*The angles of a triangle are x, y and 40°. The difference between the two angles x and y is 30°. The values of x and y are ……………..*

1️⃣ 45°, 75°
2️⃣ 50°, 80°
3️⃣ 85°, 55°
4️⃣ 55°, 95°​

Answer 1

Given :

• The angles of a triangle are$\bf\pink{x, y\: and 40°}$

• The difference between the two angles x and y is $\bf\green{30°}$

To Find :

• The values of$\bf\gray{ x\: and\: y }$

Solution :

Now let the 2 unknown angles be,

• X
• X + 30

☆ As it's mentioned that their is 30

here,

• As per the angle sum property we know that sum of interior angles in a triangle is $\bf\blue{180\degree}$

Now let's apply this property and find the angles

$\longrightarrow \sf \: 40 + x + x + 30 = 18 \\ \\ \\ \longrightarrow \sf 70 + 2x = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: 2x = 180 - 70 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf 2x = 110 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \sf \: x = \cancel{\frac{110}{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \orange{\longrightarrow \bf x = 55 \degree} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence the angles are,

• ${\bf{\pink{X = 55\degree}}}$

• ${\bf{\pink{Y =85 \degree}}}$

● So, option C is correct

Verification :

• Let's check weather their sum equals 180° to know weather we went right

$\longrightarrow \bf \: 40 + 55 + 85 = 180 \\ \\ \\ \longrightarrow \bf 40 + 140 = 180 \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \bf 180 = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Left hand side equals Right hand side

${\huge{ \sf{ \blue{ \underline{ hence \: verified }}}}} {\huge{ \blue{ \dag}}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

${\large{\underline{\rm{ Properties \:of\:triangles}}}}$

• The sum of the length of any two sides of a triangle is greater than the length of the third side.

• The side opposite to the largest angle of a triangle is the largest side.

• Any exterior angle of the triangle is equal to the sum of its interior opposite angles
• The sum of consecutive interior and exterior angle is supplementary.

• The exterior angles of a triangle always add up to 360 degrees

hope this helps ☆