Question

Hi I really need help and if possible write t he step too

Answer 1

m∠R = 118°

Step-by-step Step-by-step explanation:

Given:

• Quadrilateral PQRS is a kite.
• PQ = QR
• SP = SR
• m∠PSR = 88°
• m∠PQR = 36°

To find:

• m∠SRQ = ?

Solution:

Since one pair of opposite angles in a kite are equal, we can conclude that:

m∠SRQ = m∠SPQ

And

The 4 interior angles of a kite always sum up to 360°.

So,

m∠PSR + m∠PQR + m∠SRQ + m∠SPQ = 360°

Substitute the given value:

88° + 36° + m∠SRQ + m∠SRQ = 360°

Simplify like terms:

124° + 2m∠SRQ = 360°

Subtract 124° on both sides:

124° + 2m∠SRQ - 124° = 360° - 124°

2m∠SRQ = 236°

Divide both sides by 2.

`\sf (2m\angle SRQ)/(2) =( 236^\circ)/(2)`

m∠SRQ = 118°

So, the measure of ∠R is 118°.